Relation-theoretic metrical fixed point results via w-distance with an application in nonlinear fractional differential equations

2017/02/15 by Tanusri Senapati, Lakshmi Kanta Dey, Senapati, Tanusri +1
Mathematics · Physics and Astronomy · #47H10 #54H25 #Advanced Differential Geometry Research #FOS: Mathematics #Fixed Point Theorems Analysis #General Mathematics (math.GM) #Nonlinear Differential Equations Analysis #math.GM #msc:47H10 #msc:54H25

paper · pdf · doi:10.48550/arxiv.1702.04567

16 pages

arxiv created 2017/02/15 · openalex publication_date 2017/02/15 · arxiv updated 2017/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic metrical fixed point theory. Also, our paper consists of several non-trivial examples which signify the motivation for such investigations. Finally, our obtained results enable us to explore the existence and uniqueness of solutions of nonlinear fractional differential equations involving the Caputo fractional derivative.

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