Hybrid Proximal-Type Algorithms for Generalized Equilibrium Problems, Maximal Monotone Operators, and Relatively Nonexpansive Mappings
Lu-Chuan Zeng, Qamrul Hasan Ansari, Suliman S. Al-Homidan · Fixed Point Theory and Applications · 2010
Abstract The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set "Equation missing" of solutions of a generalized equilibrium problem, the set "Equation missing" of fixed points of a relatively nonexpansive mapping "Equation missing", and the set "Equation missing" of zeros of a maximal monotone operator "Equation missing" in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point in "Equation missing". These new results represent the improvement, generalization, and development of the previously known ones in the literature.