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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 584395, 8 pages
Research Article

Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces

1Department of Mathematics, University of Botswana, Private, Bag 00704, Gaborone, Botswana
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 21 February 2014; Accepted 7 May 2014; Published 27 May 2014

Academic Editor: Rudong Chen

Copyright © 2014 H. Zegeye and N. Shahzad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.