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
© 2014 Moosa Gabeleh, published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
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].