Strong convergence of common solutions of the fixed point sets of countable operators family and the generalized mixed equilibrium problems in Banach Spaces
Strong convergence of common solutions of the fixed point sets of countable operators family and the generalized mixed equilibrium problems in Banach Spaces
In the framework of reflexive Banach space,a new shrinking projection algorithm is proposed to approximate the common solutions of the solution of the generalized mixed equilibrium problems and the fixed point sets of a closed Bregman quasi-asymptotically nonexpansive countable operators family,and the strong convergence results of the common solutions of the solution of the gen-eralized mixed equilibrium problems and the fixed point sets of a closed Bregman quasi-asymptotically nonexpansive countable operators family are established.A numerical example of the iterative algo-rithm supporting our main results is presented.The results of Jantakarn K & Kaewcharoen A(2021)are extended and supplemented,whether the operator family is from finite to countable,or from Bregman relatively nonexpansive to Bregman quasi-asymptotically nonexpansive.
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