Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces

Strong and weak convergence of an implicit iterative process for pseudocontractive semigroups in Banach space

“…So our results improve corresponding results of many authors such as [10][11][12], of cause extend many results in [4][5][6][7][8].…”

“…Recently, the problems of convergence of an implicit iterative algorithm to a common fixed point for a family of nonexpansive mappings or pseudocontractive mappings have been considered by several authors, see [2][3][4][5]. In 2001, Xu and Ori [2] firstly introduced an implicit iterative x n = a n x n-1 + (1 -a n )T n x n , n N, x 0 C for a finite family of nonexpansive mappings {T i } N i=1 and proved some weak convergence theorems to a common fixed point for a finite family of nonexpansive mappings in a Hilbert space.…”

Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of Lipschitz pseudocontractive mappings

“…REMARK 3.1. Theorem 3.1 extends Theorem 2.6 in Chen, Song, Zhou [5] and Theorem 3.1 in Zhou [11] to the case of an implicit iteration process (see (8)) with a perturbation. Also, Theorem 3.1 holds in weaker assumptions on the space E , on the mappings T n and on the parameters {α n } than in Theorem 2 from Xu, Ori [3] and than in Theorem 2.6 from Chen, Song, Zhou [5].…”

“…Theorem 3.2 extends Theorem 2.6 in Chen, Song, Zhou [5] and Theorem 3.2 in Zhou [11] to the case of an implicit iteration process (see (8)) with a perturbation. Also, Theorem 3.2 holds in weaker assumptions on the space E , than in Theorem 2.6 in Chen, Song, Zhou [5], where E is supposed to be q -uniformly smooth and uniformly convex.…”

“…Very recently, Zhou [11] extended the above results of Chen, Song and Zhou to a more general class of real reflexive Banach space, as well as, the results of Xu and Ori to a more general class of Lipschitzian pseudocontractive mappings.…”