Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585320120240102On one-local retract in modular metrics20122010414610.48308/cgasa.2023.234064.1451ENOliver Olela OtafuduSchool of Mathematical and Statistical Sciences
North-West University, Potchefstroom Campus,
Potchefstroom 2520,
South Africa.0000-0001-9593-7899Tlotlo Odacious PhaweSchool of Mathematical and Statistical Sciences
North-West University, Potchefstroom Campus,
Potchefstroom 2520,
South Africa.0000-0003-2837-8147Journal Article20231208We 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.https://cgasa.sbu.ac.ir/article_104146_511c297d30e90fabece4a56eab1d2ef8.pdf