On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph-Reference-Cited by-同舟云学术

On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph

Published:2020-08-01 Issue: Volume:2020 Page:1-7
ISSN:0161-1712
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Saadaoui B.¹^ORCID,Lazaiz S.²^ORCID,Aamri M.¹

Affiliation:

1. Laboratory of Algebra, Analysis and Applications, Department of Mathematics, Ben M’sik Faculty of Sciences, University of Hassan II, Casablanca, Morocco

2. LASMA Laboratory, Department of Mathematics, Dhar El Mahraz Faculty of Sciences, University of Sidi Mohamed Ben Abdellah, Fes, Morocco

Abstract

We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2020/7481060.pdf

Reference12 articles.

1. Best Proximity Points of MT-Cyclic Contractions with Property UC

2. Best Proximity Point Theorems for Cyclic Relatively ρ-Nonexpansive Mappings in Modular Spaces

3. Proximal normal structure and relatively nonexpansive mappings

4. Cyclic relatively nonexpansive mappings in convex metric spaces

5. Convergence and Best Proximity Points for Generalized Contraction Pairs

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1. On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces;Moroccan Journal of Pure and Applied Analysis;2023-09-01

2. Bipartite graphs and best proximity pairs;Journal of Mathematical Sciences;2022-07