Abstract
We investigate strong convergence for Bregman strongly nonexpansive mappings by modifying Halpern and Mann’s iterations in the framework of a reflexive Banach space. As applications, we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive Banach spaces.MSC:47H05, 47H09, 47J25.
Highlights
1 Introduction Throughout this paper, we denote by N and R the sets of positive integers and real numbers, respectively
The fixed point set of T is denoted by F(T), that is, F(T) = {x ∈ C : x = Tx}
We show that the sequence {xn} is bounded
Summary
Throughout this paper, we denote by N and R the sets of positive integers and real numbers, respectively. It is known that if T is Bregman firmly nonexpansive and f is a Legendre function which is bounded, uniformly Fréchet differentiable and totally convex on bounded subsets of E, F(T) = F (T) and F(T) is closed and convex (see [ ]).
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