STRONG CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND BREGMAN QUASI-k-STRICTLY PSEUDO-CONTRACTIVE MAPPINGS IN REFLEXIVE BANACH SPACES

In this paper, we propose a new iterative method for solving the existence of common solutions of generalized mixed equilibrium problems and fixed point problems for a Bregman quasi-k-strictly pseudo-contractive mapping 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, we give a numerical example of the iterative algorithm supporting our main result.

Automated summary

This paper proposes a new iterative method for solving the existence of common solutions of generalized mixed equilibrium problems and fixed point problems for a Bregman quasi-k-strictly pseudo-contractive mapping in reflexive Banach spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the mentioned problems, with a numerical example provided to support the main result.