Abstract
This paper is devoted to the study of Ćirić-type non-unique fixed point results in modular metric spaces. We obtain various theorems about a fixed point and periodic points for a self-map on modular spaces which are not necessarily continuous and satisfy certain contractive conditions. Our results extend the results of Ćirić, Pachpatte, and Achari in modular metric spaces.
Highlights
Metric fixed point theory was initiated by the renowned theorem of Banach [1], known as the Banach Contraction Mapping Principle
Inspired by the works of Chistyakov and Ćirić, in this paper, we study non-unique fixed points and periodic points in modular metric spaces
Our results extend the results of Ćirić, Pachpatte, and Achari in modular metric spaces
Summary
Metric fixed point theory was initiated by the renowned theorem of Banach [1], known as the Banach Contraction Mapping Principle. In 1974, Ćirić [6] studied non-unique fixed point results in metric spaces He obtained various theorems about a fixed point and periodic points for a self-map f on a metric space M which is not necessarily continuous and satisfies the condition min {d( f x, f y), d( x, f x ), d(y, f y)} − min {d( x, f y), d(y, f x )} ≤ kd( x, y), where x, y ∈ M and k ∈ (0, 1). Our results extend the results of Ćirić, Pachpatte, and Achari in modular metric spaces
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