Filomat (formerly Zbornik radova Filozofskog fakulteta, serija Matematika) was founded in 1987. It is now published by the Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, and is supported by the University of Niš. Filomat is now established as an international journal of repute. The impact factor of Filomat in 2025 is 1. Filomat is a fully open access journal and does not charge any article processing charges (APCs) or submission fees. The journal publishes original papers in pure and applied mathematics. We will consider papers in the areas of expertise of our section editors that are at least 15 pages long, excluding figures. Other papers will be considered only in exceptional circumstances. Short notes or survey papers will not be considered. One author can submit at most two papers per year, including all co-authored papers. Submissions are strictly reviewed, and only papers of high quality will be accepted for publication. Usually, one volume per year consists of at least thirty issues.
Faculty of Sciences and Mathematics, University of Nis
On the order statistics from the XLindley distribution and associated inference with an application to fatigue data
In this paper, we consider the order statistics from a newly-introduced lifetime distribution, called the XLindley distribution. We have derived explicit closed form expressions for the single moments and product moments of order statistics from the XLindley distribution. Utilizing these expressions, we calculated the means, variances, and covariances of order statistics for sample sizes ranging from n = 1 to n = 10 and arbitrarily selected parameter values. Additionally, these moments allow us to identify the best linear unbiased estimators and best linear invariant estimators for the location and scale parameters, based on both complete samples and Type-II right censored samples. We also address the linear prediction of unobserved order statistics based on Type-II right-censored samples. We also explore the formulation of confidence intervals for both location and scale parameters, along with prediction intervals for unobserved order statistics. To provide comparison and illustration, we conduct a simulation study and analyze a real data example. Finally, we conclude with several remarks.
Characterizations of a space-time admitting a generalized $\varphi(Ric)$-vector
This study focuses on a generalized $\varphi(Ric)$-vector in space-times. We illustrate that a conformally flat space-time, which possesses a generalized $\varphi(Ric)$-vector that is a unit time-like vector, behaves as a perfect fluid and exhibits quasi-constant curvature under a certain condition. Additionally, we establish that this space-time can be classified as both a generalized Robertson-Walker space-time and a Robertson-Walker space-time. Furthermore, we demonstrate that this space-time represents the quintessence phase. Then, we adopt the flat Friedmann-Robertson-Walker metric to derive Hubble, jerk, deceleration and snap parameters and we observe that the null, dominant and weak energy conditions are fulfilled, but the strong energy condition has failed. Finally, we scrutinize the space-time with the generalized $\varphi(Ric)$-vector in cases it admits Ricci solitons and generalized Ricci solitons.
On the Finite-Time Blow-Up of Solutions to a Triharmonic Reaction--Diffusion Equation in Variable Exponent Sobolev Spaces
In this work, we consider a triharmonic reaction diffusion equation with a viscoelastic term. Such problems arise in diverse fields: in mathematics, in physics, phase transition, in engineering and in biology. Our primary focus is on establish upper bounds for the blow-up of solutions.
Characterization of the pseudospectrum of a compact operator
We say that a complex Banach space X belongs to the class W if for any compact operator A defined on X such that ||I +A || > 1, I +A attains norm. In this article, we characterize the pseudospectrum of any compact linear operator defined on X where X is Banach space which belongs to class W.
SUPREMUMS AND INFIMUMS OF RICCI AND SECTIONAL CURVATURES IN THE GEOMETRY OF COMPACT RIEMANNIAN MANIFOLDS
In this paper, we investigate certain numerical characteristics of an $n$-dimensional connected, compact Riemannian manifold $(M,g)$, such as supremums and infimums of its Ricci curvature~$Ric$ and sectional curvature $sec$, and explore their applications. We present two illustrative results. First, if $(M,g)$ is a compact, connected Riemannian manifold of even dimension $n=2k\geq 4$ whose the supremum and infimum of its Ricci and sectional curvatures satisfy the strict inequality $2k\, sec_{\inf}>Ric_{\sup}$, then $M$ is diffeomorphic to either the Euclidean sphere~${\mathbb S}^{2k}$ of some radius $r>0$ or the real projective space~${\mathbb R\mathbb P}^{2k}$. Second, there exists no harmonic immersion of an $n$-dimensional compact, connected Riemannian manifold $(M,g)$ into the Euclidean sphere ${\mathbb S}^m$ of radius $r>0$ if the infimum of its Ricci curvature satisfies the strict inequality $Ric _{\inf}>n/2r^2$.
compact Riemannian manifold, supremum and infimum of the sectional and the Ricci curvatures. spherical theorem, harmonic map
New Generalizations of Fractional Iyengar-Type Inequalities Involving Multi-Point Quadratures and $L_p$ Norms
In this paper, we establish several new generalizations of Iyengar-type integral inequalities within the setting of Riemann-Liouville fractional calculus. By employing a fractional version of the Montgomery identity, we derive sharp estimates for the deviation between the fractional integral of a function and its discrete weighted averages at $n$ arbitrary nodes. We extend these results to functions whose derivatives belong to the $L_r[a,b]$ spaces by utilizing H\"{o}lder's inequality. The established inequalities provide a unified setting that recovers the classical Iyengar-type results as special cases when the fractional order $\alpha=1$. Moreover, the influence of the node distribution on the associated error bounds is examined, and several corollaries corresponding to midpoint and trapezoidal-type rules are derived.
$\alpha$-limit of scalar-valued functions and related Banach spaces
In this paper, for a set $X,$ a scalar valued function $f:X\rightarrow\Bbb F,$ where $\Bbb F$ is assumed to be the set of all real or complex numbers, and for a cardinal number $\alpha,$ we define the $\alpha$-limit of $f$ as a generalization of the limit of a sequence and denote it by $\lim^{\alpha} f.$ Indeed, if we assume that $\alpha=\aleph_0$ and $X=\Bbb N,$ then $\lim^{\alpha} f$ is equal to $\lim_{n\to \infty}f(n).$ If $X$ is an infinite set and $\alpha$ an infinite cardinal number, then we define two classes of Banach spaces ${\mathfrak c}_0^{\alpha}(X)$ and ${\mathfrak c}^{\alpha}(X)$ containing all bounded functions $f:X \to \Bbb F$ which satisfy $\lim^{\alpha} f =0$ and that $\lim^{\alpha} f$ exists, respectively. Then we show that ${\mathfrak c}_0(X)\subseteq {\mathfrak c}_0^{\alpha}(X)\subseteq \ell^{\infty}(X)$ and ${\mathfrak c}(X)\subseteq {\mathfrak c}^{\alpha}(X)\subseteq \ell^{\infty}(X).$ Also, whenever the cardinal number $\alpha$ increases these spaces become larger such that the equality hold on the left sides for $\alpha =\aleph_0$ and on the right sides for all $\alpha>\card(X).$
Projectively coresolved Gorenstein flat modules over semi-trivial ring extensions
We establish necessary and sufficient conditions for modules over a semi-trivial ring extension $R\ltimes_{\Phi}M$ to be projectively coresolved Gorenstein flat. Some applications are given in the Morita context ring $\biggl(\begin{matrix} A&_{A}V_{B}\\_{B}U_{A}&B \end{matrix}\biggr)_{(\varphi,\psi)}$.
Derivations and lower cohomology of Lie algebra crossed modules
In this paper, we define the derivation of a Lie algebra crossed module and prove that it can be represented by the augmentation ideal of a crossed module. Additionally, we introduce the first cohomology groups for n = 0, 1, of a crossed module with coefficients, and we establish their connection to the classical Chevalley-Eilenberg Lie algebra cohomology.
Zalcman-Type Rescaling and Normality via TotalDerivatives in Cn
We study normal families of holomorphic functions in Cn through a generalization of Zalcman’s Lemma involving total derivatives. A new rescaling theorem is established, leading to a criterion for normality based on value separation and derivative bounds.
Normal families, Zalcman’s lemma, Total derivative, Holomorphic functions
Simpson inequalities for generalized preinvex functions under first-order differentiability
In this paper, we obtain some new Simpson's inequalities for functions whose first derivative in absolute value is r-preinvex and r-preqausi-invex (0<r<1). The results presented here contribute to the generalization and improvement of various earlier reported works. Some well-known results are highlighted as an immediate deduction of our main results.
On extremal Sombor index of bipartite graphs with given order and diameter
We consider the extremal value of the Sombor index in the class of bipartite graphs of a given order $n$ and diameter $d$. Using a layered perspective on bipartite graphs, we first derive structural lemmas and an exact formula for the Sombor index $SO(G)$ in terms of the vertex partition sizes at successive distances from a fixed vertex. This framework allows us to transform the problem into a constrained optimization, which we solve by applying concavity and convexity arguments. As a main result, we prove a comprehensive characterization of the graphs that maximize $SO(G)$ for each fixed $n$ and $d$. In particular, our results show that for $d=3$ the unique extremal graph has one vertex in each of the distance-$0$ and distance-$3$ partitions and splits the remaining $n-2$ vertices as evenly as possible between the distance-$1$ and distance-$2$ partitions. For any $d\ge 4$, the graph with maximum Sombor index is obtained by placing a single vertex in each outer distance partition while distributing the other $n-(d+1)$ vertices between two inner partitions (one of which receives $\lceil (n-d+1)/2\rceil$ vertices and the other $\lfloor (n-d+1)/2\rfloor$). These findings fill the gap in the extremal graph theory of the Sombor index under diameter constraints, extending the known case of unconstrained bipartite graphs (attaining their maximum $SO$ at $d=2$) to arbitrary prescribed diameters.
Vertex-degree-based invariants, Extremal values, Integer optimization
Solutions of a double phase singular Kirchhoff type equation with nonstandard growth
A specific category of singular class of double phase Kirchhoff type equations characterized by variable singularities is studied. By employing variational method, we prove both the uniqueness and existence of positive solutions for cases of weak variable singularities, where singularity $\eta$ lies within the interval $(0,1)$, as well as for strong variable singularities, where $\eta$ exceeds $1$. Additionally, we present an application from composite materials.
Analysis of a nonlinear Caputo fractional coupled system with integral boundary conditions in Banach spaces
In this work, we investigate a nonlinear coupled system of Caputo fractional differential equations subject to integral boundary conditions in the framework of Banach spaces. The analysis is conducted through a fixed point approach. First, the existence of mild solutions is established by employing the Kuratowski measure of noncompactness together with the Generalized Darbo's theorem involving a nondecreasing control function. Uniqueness of the solution is then obtained using the Banach contraction principle. In addition, we study the continuous dependence of the solutions on the input functions, which ensures the stability of the model under perturbations. The Ulam--Hyers stability of the system is also investigated, ensuring that small perturbations in the initial functions lead to proportionally small changes in the solution. These results contribute to the well-posedness and robustness of the proposed fractional model. Finally, a concrete example is provided to illustrate the applicability and effectiveness of the theoretical results obtained.
Error Bounds of Boole's Formula type Inequalities forGeneralized Coordinated Convex Functions with ComputationalAnalysis and Applications
This study aims to enhance the error bounds for Boole's formula-type inequalities applied to generalized coordinate convex functions. A solid mathematical foundation is established to provide improved error estimates for two-variable integrals that surpass those derived from traditional coordinate convex functions. The motivation is twofold: to extend results from convex functions to the broader class of s-convex functions and to o er optimal approximations that enhance numerical method accuracy. Moreover, Boole's formula o ers better absolute error bounds for higher-degree polynomials, especially in cases where other methods, such as Simpson's rule, fail to provide the required precision. This is due to Boole's formula's ability to approximate polynomials up to degree ve exactly, whereas Simpson's rule is limited to polynomials of degree three. Through computational analysis, key results are presented, demonstrating that the improved error bounds provide greater reliability for numerical integration applications. This research broadens the theoretical framework of mathematical analysis and optimization while providing practical methodologies to tackle real-world challenges with accuracy and e ectiveness. Future extensions of this work may include applications to q-calculus, symmetrized q-calculus, fractional calculus, and multidimensional spaces, providing deeper insights into the behavior of Boole's formula and its error bounds.
Tur\'an type inequalities for the four-parameter Mittag-Leffler type supertrigonometric functions
In this paper, we aim to investigate Tur\'an-type inequalities for the four-parameter Mittag-Leffler type supertrigonometric functions by employing a newly formulated version of the generalized Cauchy–Bunyakovsky–Schwarz (CBS) inequality. Furthermore, several significant results concerning Tur\'an-type inequalities for the generalized Wright type supertrigonometric functions are derived and established.
Generalized Mittag-Leffler functions, Generalized Wright hypergeometric function, Supertrigonometric functions, Cauchy-Bunyakovsky-Schwarz inequality, Tur\'an-type inequalities.
Mappings preserving the ascent or descent of triple skew products of operators
Let $\mathcal{B}(\mathcal{H})$ be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space $\mathcal{H}$. Let $asc(A)$ and $desc(A)$ be, respectively, the ascent and descent of an operator $A$ in $\mathcal{B}(\mathcal{H})$. In this paper, we determine the explicit form of all maps $ \phi $ from $\mathcal{B}(\mathcal{H})$ into itself that preserve the ascent or descent of triple skew product of operators.
Well-posedness and Energy Decay of Solutions to a Coupled System of Heat and Schr\"{o}dinger Equations.
Our goal is to examine a system of a Schr\"{o}dinger equation coupled with a heat equation in a bounded region. The coupling involves an operator that is parameterized by a real number in [0,1]. For $0\leq \theta<1$, we show that the associated semigroup of the system is not exponentially stable. We then propose a specific non-uniform decay rate. When $\theta= 1$, the linked semigroup is exponentially stable rather than analytic.
Uniqueness, $C_0$-Semigroup, Frequency domain approach, Analyticity of semigroups, Operators of fractional order.
A classification of restrictive polynomial correspondences
In this manuscript, we study a special class of correspondences on $\mathbb{P}^{1} \times \mathbb{P}^{1}$, namely polynomial correspondences. We focus on what we call restrictive polynomial correspondence, categorise them into reducible and irreducible ones. We further give characterising results for reducible and irreducible restrictive polynomial correspondences. We also define an operation that paves the way to obtain a new irreducible restrictive polynomial correspondence from any two given irreducible restrictive polynomial correspondences.
Reducible and irreducible correspondences
Bi Periodic Jacobsthal Polynomial Sequence and Its Various Binomial Transformations
In this study, we first introduce the bi-periodic Jacobsthal polynomial sequence. Using the elements of the bi-periodic Jacobsthal polynomial sequence, we find the generating function and Binet formula for this sequence. We also obtain some properties and sum formulas for this matrix sequence. In the main part of the study, the binomial transformations of the bi-periodic Jacobsthal polynomial sequence are obtained as a result of using the bi-periodic Jacobsthal polynomial sequence. The binomial and k-binomial transformations of the bi-periodic Jacobsthal polynomial sequence are denoted. Some relations for the binomial transformations of the bi-periodic Jacobsthal polynomial sequence are provided. In addition, the increasing and decreasing k-binomial transformations of the bi-periodic Jacobsthal polynomial sequence are given, and the recurrence formulas, Binet formulas, and generating functions of these transformation sequences are investigated.
Bi-periodic Jacobsthal sequences, Generating function, Binet formula, Binomial transformation
Second order determinants for three-term recurrence polynomial sequences
In this paper, we present some sufficient conditions for the sign of second order determinants for Hankel matrices of three-term recurrence polynomial sequences. As applications, we confirm two conjectures of Z.-H. Sun on the reverse Tur\'an expression for two polynomial sequences $G_n(x)$ and $V_n(x)$. In addition, we show that all the zeros of $G_n(x)$ and $V_n(x)$ lie on the line $\Re(x)=-1/2$.
Extremal problems on a unified family of k-uniformly starlike andconvex functions with complex order
This paper introduces and studies a new subclass of analytic functions, denoted $\mathcal{TU}_g(\kappa,b,\delta,\lambda)$, defined via the Hadamard product with a fixed function $g$. Governed by parameters $\delta \in [0, 1]$, $\kappa \geq 0$, $b \in \mathbb{C} \setminus {0}$, and $\lambda \in [0, 1)$, this class generalizes the concepts of $k$-uniformly starlike and convex functions of complex order. We establish several foundational properties for this class, including sharp coefficient bounds, radii of starlikeness and convexity, and extreme points. Furthermore, we prove subordination results, resolve Silverman's conjecture on integral means inequalities, and investigate the invariance under integral operators. Our results unify and extend numerous established theorems in geometric function theory.
$\kappa$-uniformly starlike and convex functions
On a new generalization of Stirling numbers and Bell polynomials
In this paper, we introduce and study a novel class of generalized Stirling numbers depending on a real parameter and two sequences of real numbers. This class extends several known families of numbers, including the Hsu-Shiue generalized Stirling numbers $S\left(n,k;\alpha,\beta,\gamma \right) $. We also present a combinatorial interpretation of these numbers, which allows us to derive a variety of combinatorial identities. Additionally, we establish several identities for the associated polynomials and, under suitable conditions on the defining parameters, analyze the real roots of these polynomials. Finally, we establish some properties of the differential operator acting on these polynomials.
Generalized Stirling numbers of the second kind,
A panorama of generating functions for products of classical integer sequences
In this note, we present the generating function \[ \sum_{n=0}^\infty U_{n+\ell}(x)\, U_n(y)\, t^n = \frac{(1 - t^2) \, U_\ell(x) + 2 t (t x - y) \, U_{\ell-1}(x)}{1 - 4xy\, t + 2(2x^2 + 2y^2 - 1)t^2 - 4xy\, t^3 + t^4}\,, \] where \(U_n\) denotes the Chebyshev polynomial of the second kind of order $n$ and \(\ell\) is an integer. Although this generating function can be deduced from classical results, the matrix-based derivation presented here provides a unified and alternative perspective, drawing on lesser-known references. We give a concise historical overview from algebraic, trigonometric, combinatorial, and matrix perspectives for this type of products involving Chebyshev polynomials. Particular cases and extensions are discussed. Applications to recent identities involving products of various families of well-known number sequences are also presented.
Affine nontrivial Deformation of sl(2) and osp(1/2)-Modules of
WE consider the sl(2)-module structure on the spaces of symbols of diierential operators acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given a(1)nonrelative infinitesimal deformation of this structure and prove that any a(1)nonrelative formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results. This work is the simplest generalization nonrelative of resalt by Imed Basdouri et al., in ACA MATH HUNGARICA. vol137, Issue 3, 2012.
Statistical Concentration and Failure Measures under Project–Type Refinements on Atomless Probability Spaces
In earlier work of Ili\'c and Veli\v ckovi\'c (2019) a completed project is represented by a finite set of tasks with numerical quality indices, and the overall failure of the project is measured by the largest probability assigned to any single task. Project revisions are modelled by replacing a problematic task with a family of improved subtasks, which, on the probabilistic level, corresponds to splitting one atom of a finite probability space into several smaller atoms. In this paper we give a simple measure--theoretic reformulation of this refinement procedure on a general atomless probability space. We work with finite measurable partitions and show that suitable project–type refinements, which split all atoms of maximal probability into smaller pieces of the same total probability, strictly decrease the project failure measure. Moreover, for any given threshold the failure measure can be made smaller than this threshold after finitely many such refinements, and along suitable infinite refinement sequences it converges to zero. We then introduce a natural concentration functional which measures how strongly the total failure probability is concentrated in a few atoms, and we prove that it is also strictly decreased by the same project--type refinements and can be made arbitrarily small. In this way we obtain a unified probabilistic framework in which both the maximal failure probability and a basic concentration index improve under explicit local project revisions. The original discrete project model of Ili\'c and Veli\v ckovi\'c (2019) arises as a special case, and several small project examples are given to illustrate the effect of the refinements on concrete failure profiles.
atomless probability space; statistical concentration, finite measurable partition; project–type refinement; failure measure; Rényi–type entropy; Herfindahl–Hirschman index.
On F-semi-transitive families of operators
Motivated by the concept of topological transitivity for supercyclicity, in this paper, we present the concept of Furstenberg-semi-transitivity. Then we provide sufficient conditions for cosine operator functions generated by the adjoints of weighted composition operators to be Furstenberg-semi-transitive on the space of Radon measures on a locally compact, non-compact Hausdorff space. Also, we characterize disjoint Furstenberg-semi-transitive compositions of a right multiplier and a generalized weighted bilateral shift on the standard Hilbert module over the C*-algebra of compact operators on a separable Hilbert space. As a special case, we consider the case when the corresponding Furstenberg family is the family of all infinite subsets of the set of natural numbers. Finally, we illustrate our results with concrete examples.
Furstenberg transitivity, generalized shift operator, Hilbert module, cosine operator function, Radon measures
Milne-Mercer type inequalities for h-convex functions
In this study, Milne-Mercer type inequalities for h-convex functions involving conformable operators are established. In addition, new results are presented that generalized various inequalities known in the literature.
Refinements of numerical radius estimates via the Moore–Penrose inverse
We establish new bounds for the numerical radius and generalized numerical radius of bounded operators on Hilbert spaces. By combining the Moore–Penrose inverse with elementary operator inequalities, we derive refined upper estimates that sharpen several existing results in the literature. Applications to sectorial matrices are presented, together with concrete examples illustrating the effectiveness of the obtained bounds.
A new lower bound for the doubly metric dimension and related extremal differences
In this paper a new graph invariant based on the minimum hitting set problem is introduced. It is shown that it represents a tight lower bound for the doubly metric dimension of a graph. Exact values of this new invariant for paths, cycles, stars, complete graphs and complete bipartite graphs are obtained. The paper analyzes certain tight bounds for the new invariant in general case. Also, several extremal differences between some related invariants are determined.
Doubly metric dimension, Hitting set problem, Metric dimension, Extremal differences.