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

Nihal TaşORCID record, Ayşenur ŞenORCID record
An introduction to the fixed-circle problem with metric-preserving functions
Mathematica Moravica, Vol. 30, No. 1 (2026), 1–17.
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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 BoukerORCID record, Taieb HamaiziaORCID record, Deep ChandORCID record, Yumnam RohenORCID record
Fixed point theorems for paired contractions in $b$-metric spaces
Mathematica Moravica, Vol. 30, No. 1 (2026), 19–30.
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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 JoshiORCID record, Naveen ChandraORCID record
On weak orbitally and asymptotically continuous mappings
Mathematica Moravica, Vol. 30, No. 1 (2026), 31–39.
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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 LimanORCID record, Refik KeskinORCID record, Merve GüneyORCID record
Some new identities for the sum of generalized Fibonacci numbers and generalized Lucas numbers
Mathematica Moravica, Vol. 30, No. 1 (2026), 41–60.
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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. BalachandranORCID record
Existence of solutions of a class of fractional partial integrodifferential equations
Mathematica Moravica, Vol. 30, No. 1 (2026), 61–70.
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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.