Mathematica Moravica, Vol. 29, No. 2 (2025)

Michael Gil'ORCID record
Bounds for the functional spectrum of operators in a Hilbert space
Mathematica Moravica, Vol. 29, No. 2 (2025), 1–11.
doi: https://doi.org/10.5937/MatMor2502001G
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Abstract. Let $\mathcal{H}_1$ and $\mathcal{H}_2$ be Hilbert spaces with the unit operators $I_1$ and $I_2$, respectively, and $A_{jk}$ be bounded operators acting from $\mathcal{H}_j$ into $\mathcal{H}_k$ $(j,k=1,2)$. We consider the block operator matrices $A=(A_{jk})$ and $F(z)={\rm diag} (\hat{K}_j(z)I_{j})$, where $\hat{K}_1(z)$ and $\hat{K}_2(z)$ are scalar analytic functions. The set of all $z\in\mathbb{C}$, such that $F(z)-A$ is boundedly invertible is called the $F$-regular set of $A$. The complement of the $F$-regular set to the complex plane is called the $F$-spectrum (the functional spectrum) of $A$. It is shown that the notion of the functional spectrum enables us to investigate, from the unified point of view, various types of coupled systems, in particular, systems of integral, fractional differential, integro-differential and differential-difference equations. We derive a bound for the functional spectrum and discuss applications of the obtained bound to the stability of the considered systems.
Keywords. Hilbert space, functional spectrum, operators, integral equations, fractional differential equations, stability.

Kikunga Kasenda IvanORCID record
On a family of hypergeometric polynomials
Mathematica Moravica, Vol. 29, No. 2 (2025), 13–31.
doi: https://doi.org/10.5937/MatMor2502013K
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Abstract. We work with sequences of integrals that we call SCE integrals. We establish their expressions in terms of five families of polynomials. We demonstrate the relations between these integrals and we focus on one of the three integrals: the determination of the family of polynomials noted $e_n$ $(n \in \mathbb{N})$. We show that these polynomials are hypergeometric. From this property, the NU method can be applied to this family. We determine the Rodrigues formula. These polynomials have properties that distinguish them from classical hypergeometric polynomials. We state and demonstrate the theorem adapted to the determination of the $e_n$ generating function. Finally, the sequence of polynomials studied is expressed in terms of associated Laguerre polynomials with negative upper indices.
Keywords. NU Method, SCE Integrals, Hypergeometric polynomials, Rodrigues Formula, Generating Function, Truncated Exponential Polynomials.

Deepak KhantwalORCID record, J.L. MamaboloORCID record, Rajendra PantORCID record
Viscosity approximations with $\varphi$-contractive mappings
Mathematica Moravica, Vol. 29, No. 2 (2025), 33–48.
doi: https://doi.org/10.5937/MatMor2502033D
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Abstract. This paper investigates the viscosity approximation method with a general class of $\varphi$-contractive mappings. We demonstrate that Moudafi’s viscosity approximation scheme can be derived from Browder and Halpern-type convergence theorems. Our results extend several existing convergence theorems. Finally, we present a series of deduced results based on these findings. We also present an application of the obtained results to split feasibility problems.
Keywords. Fixed point, nonexpansive mappings, Viscosity approximation, Split feasibility problem.

Paula CatarinoORCID record, Anabela BorgesORCID record, Paulo VascoORCID record, Elen SpreaficoORCID record, Eudes CostaORCID record
On the norms and Hadamard product of Toeplitz matrices involving Leonardo numbers
Mathematica Moravica, Vol. 29, No. 2 (2025), 49–66.
doi: https://doi.org/10.5937/MatMor2502049C
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Abstract. In this study, we consider the Toeplitz matrices with entries being Leonardo numbers. We have found upper and lower bounds for the spectral norms of these matrices, considering also the Hadamard product of this type of matrix.
Keywords. Fibonacci numbers, Leonardo numbers, Toeplitz matrix, Spectral norm, Euclidean norm, Hadamard product.

Şeyda SezgekORCID record, İlhan DağadurORCID record
$\nu-$Wedge FDK-spaces
Mathematica Moravica, Vol. 29, No. 2 (2025), 67–82.
doi: https://doi.org/10.5937/MatMor2502067S
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Abstract. The (weak) wedgeness for FK-spaces was first defined by Bennett in 1974. Then, some results of Bennett (1974) were improved by İnce (2002) and Dağadur (2004) for all (weak) wedge FK spaces. In this paper, the concept of wedgeness for an FDK-space $X$ containing $\Phi$ is defined, and some fundamental characterizations related to this space and compactness of the inclusion mapping are studied. Also, some results for a summability domain $X_A^{(\nu)}$ to be (weak) $\nu-$wedge are obtained. Moreover, necessary and sufficient conditions for some double sequence spaces are given.
Keywords. Double sequence, FDK-space, wedge FK-space.

Kishan S. DaniORCID record, N. ChandraORCID record, Mahesh C. JoshiORCID record, S. RawatORCID record
Some metric fixed point theorems for weakly orbitally continuous mappings
Mathematica Moravica, Vol. 29, No. 2 (2025), 83–93.
doi: https://doi.org/10.5937/MatMor2502083K
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Abstract. The purpose of this paper is to establish some fixed point results on the complete and orbitally complete metric spaces for Ćirić type contractive mappings in the context of weakly orbital continuity. Also, the concept of asymptotically regular mapping is used for the existence of fixed points. However, our results generalize several well known results in the literature. Additionally, we have presented our theorems through some non-trivial examples, and an application to integral equations has also provided.
Keywords. Asymptotic regularity, fixed point, orbital completeness, orbital continuity, $k$-continuity and weakly orbital continuity.

Emre TaşORCID record, Selma EkiciORCID record
Multivariate trigonometric Korovkin theorem within a fuzzy framework
Mathematica Moravica, Vol. 29, No. 2 (2025), 95–101.
doi: https://doi.org/10.5937/MatMor2502095E
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Abstract. In this paper, the trigonometric fuzzy Korovkin theorem, originally established by G. A. Anastassiou and S. G. Gal (Nonlinear Functional Analysis and Applications, 11 (2006), 385–395), is extended to the $k$-dimensional setting. The proof is based on a new approach that differs from the original one and does not rely on the fuzzy modulus of continuity. An illustrative example is included to confirm the applicability and validity of the proposed generalization.
Keywords. Fuzzy calculus, Trigonometric Korovkin theorem, Fuzzy positive linear operator.

Jawher KhmiriORCID record
A note on infinitely divisible distribution on function fields
Mathematica Moravica, Vol. 29, No. 2 (2025), 103–115.
doi: https://doi.org/10.5937/MatMor2502103J
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Abstract. In this note, we define a function associated with the zeta function on function fields of genus $g$ over a finite field $\mathbb{F}_q$. We shown that the exponential of this function is the characteristic function of an infinitely divisible distribution on the real line, which is equivalent to the Riemann hypothesis on function fields. Furthermore, we give some special values of this characteristic function and derive several interesting summation formulas.
Keywords. Characteristic function, Infinitely divisible distribution, Lévy-Khintchine formula, Riemann zeta-function, Function fields, Generalized Riemann hypothesis.

S. A. M. MohsenailhosseiniORCID record, M. SaheliORCID record
G-approximate best proximity pairs in metric space with a directed graph
Mathematica Moravica, Vol. 29, No. 2 (2025), 117–129.
doi: https://doi.org/10.5937/MatMor2502117M
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Abstract. Let $(X,d)$ be a metric space endowed with a directed graph $G$ where $V(G)$ and $E(G)$ represent the sets of vertices and edges corresponding to $X$, respectively. We establish sufficient conditions for the existence of a $G$-approximate best proximity pair for a mapping $T$ in the metric space $X$ equipped with the graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$.
Keywords. G-approximate best proximity pairs, G-approximate best minimizing sequences, Connected graph, G-T-minimizing.

Tatjana MirkovićORCID record, Nataša ĆirovićORCID record
On a new Laplace transform formula for shift properties on time scale
Mathematica Moravica, Vol. 29, No. 2 (2025), 131–144.
doi: https://doi.org/10.5937/MatMor2502131M
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Abstract. We give a new formula of the Laplace transform expressed using the delta derivative for the generalized time scales. This formula \[ F\left( z \right)_\mathbb{T}= \mathscr{L}_{\mathbb{T}} \left\{ {f\left( t \right)} \right\}\left( z \right) = \int_0^\infty {ze_{ \ominus \left( {z - 1} \right)} \left( {\sigma \left( t \right),0} \right)f\left( t \right)\Delta t} \] combines the theory of classical Laplace and $\mathscr{Z}$ transforms. By choosing the time scale to be a set of real numbers, the classical Laplace transformation is obtained in a modified form, and if the time scale is chosen to be a set of integers, the classical $\mathscr{Z}$ transformation is obtained. Formulas for the Laplace transform of elementary functions, as well as formulas for real and complex shifting properties, are derived. These formulas are introduced for specific functions.
Keywords. Time Scale, $\Delta$ derivative, Laplace transform, $\mathscr{Z}$-transform, Shift properties.