Best proximity point theorems in b-metric spaces

Best proximity point theorems in b-metric spaces In this paper, we prove best proximity point theorems for types of cyclic b-contrac- tion mappings in the setting of complete b-metric spaces which generalize some results in the current literature. Keywords Fixed point · Best proximity point · Complete metric space · Contraction · b-Metric space Mathematics Subject Classification 46N40 · 47H10 · 54H25 1 Introduction and preliminaries The fixed point theory plays a vital role in mathematical analysis. Best approxima - tions and best proximity points are considered as an extension of fixed point theory. In 1922, Stefan Banach has come up with beautiful theorem known as banach con- traction theorem. This theorem laid foundation for all fixed point theorems. Eldred and Veeramani [1] proved existence and convergence of best proximity points in 2006. Then, many authors presented best proximity point results for different types of mappings [2–5]. In this section, we provide some basic definitions. Define dist(A, B)= inf{d(a, b)∶ a ∈ A, b ∈ B} A ={a ∈ A ∶ d(a, b)= dist(A, B) for some b ∈ B} B ={b ∈ B ∶ d(a, b)= dist(A, B) for some a ∈ A} * J. Maria Joseph joseph80john@gmail.com J. Beny benykutty@gmail.com M. Marudai marudaim@yahoo.co.in Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli 620 002, India Department of Mathematics, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Best proximity point theorems in b-metric spaces

, Volume OnlineFirst – Nov 28, 2018
8 pages

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Publisher
Springer Journals
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0151-0
Publisher site
See Article on Publisher Site

Abstract

In this paper, we prove best proximity point theorems for types of cyclic b-contrac- tion mappings in the setting of complete b-metric spaces which generalize some results in the current literature. Keywords Fixed point · Best proximity point · Complete metric space · Contraction · b-Metric space Mathematics Subject Classification 46N40 · 47H10 · 54H25 1 Introduction and preliminaries The fixed point theory plays a vital role in mathematical analysis. Best approxima - tions and best proximity points are considered as an extension of fixed point theory. In 1922, Stefan Banach has come up with beautiful theorem known as banach con- traction theorem. This theorem laid foundation for all fixed point theorems. Eldred and Veeramani [1] proved existence and convergence of best proximity points in 2006. Then, many authors presented best proximity point results for different types of mappings [2–5]. In this section, we provide some basic definitions. Define dist(A, B)= inf{d(a, b)∶ a ∈ A, b ∈ B} A ={a ∈ A ∶ d(a, b)= dist(A, B) for some b ∈ B} B ={b ∈ B ∶ d(a, b)= dist(A, B) for some a ∈ A} * J. Maria Joseph joseph80john@gmail.com J. Beny benykutty@gmail.com M. Marudai marudaim@yahoo.co.in Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli 620 002, India Department of Mathematics,

Journal

The Journal of AnalysisSpringer Journals

Published: Nov 28, 2018

References

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