Best proximity point results in \(b\)-metric space and application to nonlinear fractional differential equation
type: Item
instance of: scholarly article
title: Best proximity point results in \(b\)-metric space and application to nonlinear fractional differential equation
author: Azhar Hussain
author: Tanzeela Kanwal
author: Muhammad Adeel
author: Stojan Radenović
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: Based on the concepts of contractive conditions due to Suzuki (Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 2008, 136, 1861-1869) and Jleli (Jleli, M., Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014, 2014, 38), our aim is to combine the aforementioned concepts in more general way for set valued and single valued mappings and to prove the existence of best proximity point results in the context of \(b\)-metric spaces. Endowing the concept of graph with \(b\)-metric space, we present some best proximity point results. Some concrete examples are presented to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear fractional differential equation involving Caputo derivative. Presented results not only unify but also generalize several existing results on the topic in the corresponding literature.
Mathematics Subject Classification ID: 47-XX
Mathematics Subject Classification ID: 26-XX
zbMATH DE Number: 6994824
zbMATH Keywords: Suzuki-contraction
zbMATH Keywords: \(b\)-metric space
zbMATH Keywords: Caputo derivative
MaRDI profile type: Publication
full work available at URL: math6110221
OpenAlex ID: W2898444857
Wikidata QID: Q115221226
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DOI: 10.3390/MATH6110221
description: scientific article; zbMATH DE number 6994824