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In this paper, a two-steps modifying Halpern iteration for Bregman strongly nonexpansive multi-valued mappings in the framework of reflexive Banach spaces is established. Under suitable limit conditions, some strong convergence theorems for this iteration are proved. We apply our main results to solve classical 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), Li et al. (Fixed Point Theory Appl. 2013:197, 2013) and Chang and Wang (Appl. Math. Comput. 228:38-48, 2014).

journal of inequalities and applications

Strong convergence results of two-steps modifying Halpern’s iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application