Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets

Nuttawut Bunlue; Suthep Suantai

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 3, page 165-176
  • ISSN: 0044-8753

Abstract

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In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in the literatures.

How to cite

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Bunlue, Nuttawut, and Suantai, Suthep. "Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets." Archivum Mathematicum 054.3 (2018): 165-176. <http://eudml.org/doc/294659>.

@article{Bunlue2018,
abstract = {In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in the literatures.},
author = {Bunlue, Nuttawut, Suantai, Suthep},
journal = {Archivum Mathematicum},
keywords = {best proximity point; proximal weak contraction mapping; proximal Berinde nonexpansive mapping; starshaped set},
language = {eng},
number = {3},
pages = {165-176},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets},
url = {http://eudml.org/doc/294659},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Bunlue, Nuttawut
AU - Suantai, Suthep
TI - Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 3
SP - 165
EP - 176
AB - In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in the literatures.
LA - eng
KW - best proximity point; proximal weak contraction mapping; proximal Berinde nonexpansive mapping; starshaped set
UR - http://eudml.org/doc/294659
ER -

References

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