<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasi-normal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. Convex Anal. 14 (2013), 653-659].</p></abstract>

We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasi-normal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. Convex Anal. 14 (2013), 653-659].

Proximal quasi-normal structure in convex metric spaces

Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Proximal quasi-normal structure in convex metric spaces"}

We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity...

Proximal quasi-normal structure in convex metric spaces

Published Online: Dec 22, 2015

Page range: 45 - 58

Received: May 01, 2013

Accepted: Jul 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0049

Keywords
Best proximity point, proximal quasi-normal structure, relatively Kannan nonexpansive mapping, convex metric space

© 2014 Moosa Gabeleh, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Proximal quasi-normal structure in convex metric spaces

Published Online: Dec 22, 2015

Page range: 45 - 58

Received: May 01, 2013

Accepted: Jul 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0049

KeywordsBest proximity point, proximal quasi-normal structure, relatively Kannan nonexpansive mapping, convex metric space

© 2014 Moosa Gabeleh, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Best proximity point, proximal quasi-normal structure, relatively Kannan nonexpansive mapping, convex metric space