The purpose of this paper is to suggest a new algorithm for finding a common solution of a mixed equilibrium problem and a common fixed point of uniformly Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces. The strong convergence theorems under suitable control conditions are proven.
In this paper, we propose a new iterative method for solving the mixed equilibrium problems and the fixed point problems for a countable family of Bregman relatively nonexpansive mappings in reflexive Banach spaces. We prove that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the mentioned problems. Further, a numerical example of the iterative algorithm supporting our main result is presented.
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