<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper explores the concept of normal structure by introducing a generalized form known as <italic>P</italic>-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively <italic>P</italic>-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context.</p>
</abstract>

This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively P-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context.

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

Hassan II University of Casablanca, Faculty of Sciences Ben M’Sik

Laboratory of Analyse Modelisation and Simulation

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of...

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

Publié en ligne: 29 sept. 2023

Pages: 339 - 353

Reçu: 30 sept. 2022

Accepté: 28 août 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0023

Mots clés
Best proximity point, Hausdorff locally convex space, cyclic mapping, noncyclic mapping, relatively -nonexpansive mapping, probabilistic normed space, -normal structure

© 2023 Brahim Saadaoui et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

Publié en ligne: 29 sept. 2023

Pages: 339 - 353

Reçu: 30 sept. 2022

Accepté: 28 août 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0023

Mots clésBest proximity point, Hausdorff locally convex space, cyclic mapping, noncyclic mapping, relatively -nonexpansive mapping, probabilistic normed space, -normal structure

© 2023 Brahim Saadaoui et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Best proximity point, Hausdorff locally convex space, cyclic mapping, noncyclic mapping, relatively -nonexpansive mapping, probabilistic normed space, -normal structure