On one-local retract in modular metrics

Document Type : Research Paper

Authors

School of Mathematical and Statistical Sciences North-West University, Potchefstroom Campus, Potchefstroom 2520, South Africa.

10.48308/cgasa.2023.234064.1451

Abstract

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.

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References

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Categories and General Algebraic Structures with Applications
Volume 20, Issue 1
Special Issue Dedicated to Prof. Themba Dube
January 2024
Pages 201-220

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