On split equality generalized equilibrium problems and fixed point problems of Bregman relatively nonexpansive semigroups
Journal of Applied and Numerical Optimization · 2022
In this paper, we introduce a new split inverse problem called the split equality generalized equilibrium problem which is more general than the split feasibility problem, the split equilibrium problem, and the split equality equilibrium problem.We develop an iterative algorithm for approximating a common solution of this problem and the split equality fixed point problem for Bregman relatively nonexpansive semigroups in p-uniformly convex and uniformly smooth Banach spaces.Using our iterative algorithm, we prove a strong convergence theorem and investigate a split equality convex optimization problem as an application.Finally, we present some numerical experiments to demonstrate the applicability of our proposed method.