Abstract
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).
Highlights
Let D be a nonempty and closed subset of a real Banach space X
The set of fixed points of T is denoted by F(T)
The results presented in the paper improve and extend the corresponding results in [ ]
Summary
Let D be a nonempty and closed subset of a real Banach space X. It is known that if T is Bregman firmly nonexpansive and f is the Legendre function which is bounded, uniformly Fréchet differentiable and totally convex on bounded subsets of X, F(T) = F (T) and F(T) is closed and convex (see [ ]).
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