Extragradient methods for split feasibility problems and generalized equilibrium problems in Banach spaces

Abstract

The purpose of this paper is the presentation of a new extragradient algorithm in 2-uniformly convex real Banach spaces. We prove that the sequences generated by this algorithm converge strongly to a point in the solution set of split feasibility problem, which is also a common element of the solution set of a generalized equilibrium problem and fixed points of of two relatively nonexpansive mappings. We give a numerical example to investigate the behavior of the sequences generated by our algorithm.KEYWORDS generalized equilibrium problem, generalized metric projection, relatively nonexpansive mapping, split feasibility problem, variational inequality

The split common null point problem for generalized resolvents and nonexpansive mappings in Banach spaces

“…there exists a fixed constant c > 0 such that ρ E (t) ≤ ct q , then E is said to be q-uniformly smooth, see [19]. It is well known that a uniformly convex Banach space is reflexive and strictly convex.…”

A simple proof for Kazmi et al.'s iterative scheme

“…To see the denitions of maximal monotone operators and α-inverse strongly monotone mappings one can refer to for example [1,2,3,4,6,7,8]. The following theorem have been proved in [5,Theorem 3.1 ].…”

Strong convergent iterative techniques for 2-generalized hybrid mappings and split equilibrium problems

“…The split equilibrium problem (1)-(2) constitute a pair of equilibrium problems where is the generalization of split feasibility problems. Some iterative methods have been rapidly established for solving these problems (see [1][2][3][4][5][6][7][8][9][10]).…”