Abstract
In this paper, we introduce the concept of coincidence best proximity point for multivalued Suzuki-type α -admissible mapping using θ -contraction in b-metric space. Some examples are presented here to understand the use of the main results and to support the results proved herein. The obtained results extend and generalize various existing results in literature.
Highlights
Introduction and PreliminariesIn 1922, Stefan Banach [1] proved his famous result “Banach contraction principle”, which states that “let ( X, d) be a complete metric space and T : X → X be a contraction, T has a unique fixed point”.The constructive proof of theorem helps the researchers working in Computer Sciences to develop algorithm based upon the proof of theorem, and it able them to solve complex networking problem by relating it with “fixed point problem”
“Banach fixed point theorem”, weak contractive conditions were introduced for finding unique “fixed point”. Often these weak conditions are related with metric spaces and some time are related with contractive conditions
In generalization of contractive conditions, the existence and convergence of best proximity points were discussed by various author
Summary
Naeem Saleem 1 , Jelena Vujaković 2, *, Wali Ullah Baloch 1 and Stojan Radenović 3,4, *. Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia. Nonlinear Analysis research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam. Received: 19 September 2019; Accepted: 22 October 2019; Published: 25 October 2019
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