Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces

On problem of nearest common fixed point of nonexpansive mappings

“…The results presented in the paper extend and improve some recent results in Xu [7] , O'Hara et al [5] , Song et al [6] , Jung [4] , Chang [3] , Shioji et al [8] and Shimizu et al [9] . For the sake of convenience, we first recall some definitions, notations and conclusions.…”

“…In this section we shall utilize Theorem 2.2 to deduce some recent results of Shimizu and Takahashi [9] , O'Hara et al [5] , Song, Chen and Zhou [6] as its corollaries. T j x, n ≥ 1.…”

“…[1][2][3][4][5][6][7] and the references therein). The purpose of this paper is to study the convergence problem of the iterative scheme (1) for an infinite family of nonexpansive mappings T 1 , T 2 , · · · and a given contractive mappin f in a reflexive Banach space.…”

Some extragradient methods for common solutions of generalized equilibrium problems and fixed points of nonexpansive mappings

“…Inspired by the ideas in [1][2][3][4][5][6][8][9][10][11][12][13][14][15][16]22] and the references therein, we introduce some new iterative schemes based on the extragradient method (and the hybrid method) for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for a monotone, Lipschitz-continuous mapping without using the W-mapping generated by a family of infinitely (finitely) nonexpansive mappings. We obtain both strong convergence theorems and weak convergence theorems for the sequences generated by the corresponding processes.…”

A composite iterative algorithm for common fixed points for a finite family of nonexpansive mappings and applications

“…In the last twenty years or so, many papers have been written on the existence and convergence of fixed points for nonlinear mappings, and strong and weak convergence theorems have been obtained by using some well-known iterative processes (see, e.g., [4][5][6]3,[7][8][9][10][11][12][13]1,2,[14][15][16][17][18][19][20]). Recall that the so-called problem of image recovery is essential for finding a common element for finitely many nonexpansive retraction K 1 , K 2 , .…”