%0 Journal Article
%T On one-local retract in modular metrics
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Olela Otafudu, Oliver
%A Phawe, Tlotlo Odacious
%D 2024
%\ 01/02/2024
%V 20
%N 1
%P 201-220
%! On one-local retract in modular metrics
%K fixed point
%K one local retract
%K normal structure
%K $w$-admissible
%R 10.48308/cgasa.2023.234064.1451
%X We continue the study of the concept of one local retract in the settings of modular metrics. This concept has been studied in metric spaces and quasi-metric spaces by different authors with different motivations. In this article, we extend the well-known results on one-local retract in metric point of view to the framework of modular metrics. In particular, we show that any self-map $\psi: X_w \longrightarrow X_w$ satisfying the property $w(\lambda,\psi(x),\psi(y)) \leq w(\lambda,x,y)$ for all $x,y \in X$ and $\lambda >0$, has at least one fixed point whenever the collection of all $q_w$-admissible subsets of $X_{w}$ is both compact and normal.
%U https://cgasa.sbu.ac.ir/article_104146_511c297d30e90fabece4a56eab1d2ef8.pdf