AN ITERATIVE METHOD FOR SOLVING SPLIT GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES

作者：Ogbuisi F. U.^*

来源：Journal of Nonlinear and Convex Analysis, 2018, 19(5): 803-821.

• Strong convergence
• split generalised mixed equilibrium problem
• P-Uniformly convex
• uniformly smooth
• Bregman distance
• Bregman strongly nonexpansive mapping

Our aim in this paper is to study split generalised mixed equilibrium and fixed point problems in a real Banach space with a view to analyze an iterative method for obtaining a solution of the split generalised mixed equilibrium problem and fixed point problem in a real Banach space using the Bregman distance approach. Furthermore, we introduce an iterative algorithm for approximating a common solution of split generalised mixed equilibrium problem and a fixed point problem for left Bregman strongly nonexpansive mapping and with our algorithm, we state and prove a strong convergence theorem for the approximation of a common element of the set of solutions of a split generalised mixed equilibrium problem and the set of solutions of a fixed point problem in the framework of a p-uniformly convex Banach space which is also uniformly smooth. Our result extends existing results on split equilibrium problems in the literature from the framework of real Hilbert spaces to p-uniformly convex Banach spaces which are also uniformly smooth.

• 出版日期2018