Halpern’s iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application
Yi Li, Hongbo Liu, Kelong Zheng · Fixed Point Theory and Applications · 2013
Bregman strongly nonexpansive multi-valued mapping in reflexive Banach spaces is established. Under suitable limit conditions, some strong convergence theorems for modifying Halpern’s iterations are proved. As an application, we utilize the main results to solve equilibrium problems in the framework of reflexive Banach spaces. The main results presented in the paper improve and extend the corresponding results in the work by Suthep et al. (Comput. Math. Appl. 64:489-499, 2012). MSC: 47J05, 47H09, 49J25.