Mathematica Moravica, Vol. 30, No. 1 (2026)

Nihal Taş, Ayşenur Şen
An introduction to the fixed-circle problem with metric-preserving functions
Mathematica Moravica, Vol. 30, No. 1 (2026), 1–17.
doi: https://doi.org/10.5937/MatMor2601001T
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Abstract. There are many studies in the literature about both the concept of a metric-preserving function and the fixed-circle problem. In this paper, we obtain new fixed-circle theorems by using these two concepts together. We support the theoretical results we obtained with necessary examples. The importance of this study is that it contains the first fixed-circle theorems obtained using the metric-preserving function concept.
Keywords. Metric space, Metric-preserving function, Fixed circle.

Zouhir Idriss Bouker, Taieb Hamaizia, Deep Chand, Yumnam Rohen
Fixed point theorems for paired contractions in $b$-metric spaces
Mathematica Moravica, Vol. 30, No. 1 (2026), 19–30.
doi: https://doi.org/10.5937/MatMor2601019I
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Abstract. In this research, we establish new fixed-point theorems for mappings that satisfy the paired contraction property in $b$-metric spaces. Our results extend and generalize several well-known fixed-point theorems in the literature.
Keywords. $b$-metric spaces, Fixed point, Paired contraction.

Bharti Joshi, Naveen Chandra
On weak orbitally and asymptotically continuous mappings
Mathematica Moravica, Vol. 30, No. 1 (2026), 31–39.
doi: https://doi.org/10.5937/MatMor2601031J
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Abstract. In this note, we show that the recent results due to Khan and Oyetunbi [J. Fixed Point Theory Appl. 22:47, 2020], Górnicki [J. Fixed Point Theory Appl. 22:8, 2020], Bisht [J. Fixed Point Theory Appl. 21:54, 2019] and Górnicki [J. Fixed Point Theory Appl. 21:29, 2019] are still valid if mappings are not necessarily orbitally continuous or $k$-continuous on a complete metric space, but satisfy the weaker version of orbital continuity and $k$-continuity.
Keywords. Orbitally continuous, $T$-orbitally lower semi-continuous, Weak orbitally continuous, $k$-continuous, Asymptotically continuous, Asymptotically regular.

Gülsüm Liman, Refik Keskin, Merve Güney
Some new identities for the sum of generalized Fibonacci numbers and generalized Lucas numbers
Mathematica Moravica, Vol. 30, No. 1 (2026), 41–60.
doi: https://doi.org/10.5937/MatMor2601041L
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Abstract. Let $U_n$ and $V_n$ denote the $n$-th generalized Fibonacci and generalized Lucas numbers, respectively. In this paper, we calculate the $n$-th powers of some square matrices by diagonalizing them with their eigenvalues and eigenvectors. We find some terms of these matrices as generalized Fibonacci numbers and generalized Lucas numbers. Using matrix powers and the binomial theorem, we give some new identities. Finally, we show again that the known identity $(k^{2}+4t)(-t)^{n-1}=V_{n+1}V_{n-1}-V_{n}^{2}$ where is satisfied with the help of the obtained matrices.
Keywords. Fibonacci number, Lucas number, Generalized Fibonacci sequence, Generalized Lucas sequence, Matrix equations and identities.

K. Balachandran
Existence of solutions of a class of fractional partial integrodifferential equations
Mathematica Moravica, Vol. 30, No. 1 (2026), 61–70.
doi: https://doi.org/10.5937/MatMor2601061B
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Abstract. In this paper we study the existence of solutions for the nonlinear Sobolev type fractional partial integrodifferential equations with Neumann boundary condition. Under suitable assumptions the results are established by using the Leray-Schauder fixed point theorem.
Keywords. Fractional partial integrodifferential equations, Sobolev-type, Existence of solutions.

Nataša Pavlović Komazec
On the regularized trace formula for a Sturm–Liouville boundary value problem with two delays and two potentials
Mathematica Moravica, Vol. 30, No. 1 (2026), 71–81.
doi: https://doi.org/10.5937/MatMor2601071P
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Abstract. This paper is devoted to a Sturm–Liouville boundary value problem with two constant delays $\tau_1,\tau_2\in[\pi/3,\pi)$ and two potentials $q_1,q_2\in L_2[0,\pi]$. We derive an asymptotic expansion of the characteristic function and obtain asymptotic formulas for the eigenvalues. Using the Lidskii–Sadovnichii contour integration method, we establish an explicit formula for the first regularized trace of the corresponding operator.
Keywords. Differential operators with delays, Sturm–Liouville operator, Regularized trace formula.

Hikmat I. Ahmadov, Diego Julio Cirilo-Lombardo
On one mixed problem for parabolic type equation with constant coefficients
Mathematica Moravica, Vol. 30, No. 1 (2026), 83–102.
doi: https://doi.org/10.5937/MatMor2601083A
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Abstract. The problem of the parabolic equation with constant coefficients and time displacement is investigated under non-local and non-homogeneous boundary conditions. Under minimal conditions on the data, the uniqueness of the solution is demonstrated and an explicit analytical representation of it is obtained.
Keywords. Parabolic type equations, Mixed problems, Non-local and non-homogeneous boundary conditions.

Ajay Kumar Sharma, Manjari Dewangan, M.P. Goswami
Best proximity point results for $p$-semi-cyclic contraction pair in Banach spaces
Mathematica Moravica, Vol. 30, No. 1 (2026), 103–114.
doi: https://doi.org/10.5937/MatMor2601103K
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Abstract. In the present work, we extend the semi-cyclic contraction conditions established by Gabeleh and Abkar [9] by introducing the concept of a $p$-semi-cyclic contraction for a pair of mappings $(S,T)$ on the union of $p(\geq 2)$ nonempty subsets in a Banach space. In the sequel, we establish several fundamental results, including existence and convergence theorems for best proximity points corresponding to the pair $(S,T)$. Additionally, illustrative examples are provided to support our findings.
Keywords. Cyclic contraction, $p$-semi-cyclic contraction, Best proximity point, Fixed point.

Hugo Leiva, Cosme Duque, Marcial Valero
Controllability of impulsive semilinear pure integro-differential equations with delays and nonlocal conditions
Mathematica Moravica, Vol. 30, No. 1 (2026), 115–130.
doi: https://doi.org/10.5937/MatMor2601115L
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Abstract. In this paper, we study the exact and approximate controllability of a class of semilinear integro-differential control systems involving impulses, delays, and nonlocal conditions. In contrast to standard approaches, where the corresponding linear dynamics are transformed into an ordinary differential equation and memory effects are incorporated as perturbations, we preserve the original Volterra integro-differential structure of the system. Our approach starts with a detailed analysis of the controllability properties of the associated linear integro-differential system. Based on this characterization, we then address the semilinear problem. Under appropriate assumptions on the nonlinear contributions, including those induced by delay-dependent terms, impulsive effects, and nonlocal conditions, we establish exact controllability by employing Rothe's fixed-point theorem and a suitable subadditivity framework. Furthermore, by weakening the conditions imposed on the nonlinear terms, we obtain approximate controllability results through an alternative technique inspired by A.E. Bashirov et al., which allows us to avoid the use of fixed-point arguments.
Keywords. Controllability, Integro-differential equation, Delay, Impulses, Nonlocal conditions.

Mladen Janjić, Marija Đukić, Vučelja Lekić, Katarina Pavlović
Approximate reasoning from sampled data
Mathematica Moravica, Vol. 30, No. 1 (2026), 131–140.
doi: https://doi.org/10.5937/MatMor2601131J
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Abstract. The subject of this paper is a mathematical framework that provides a basis and a tool for reasoning about uncertainty based on linguistic information.
Keywords. Linguistic variable, Words, Natural language, Fuzzy rule based systems.