On one-local retract in modular metrics

Document Type : Research Paper


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



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.


Main Subjects

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