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Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

Temir S.

Demonstratio Mathematica

2013

Vol. 46, nr 4

781--793

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicititeration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Saluja G. S., Nashine H. K.

Opuscula Mathematica

2010

Vol. 30, no. 3

331-340

In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.

Strong convergence of an implicit iteration process for a finite family of quasi-contractive operators

Rafiq A.

Demonstratio Mathematica

2007

Vol. 40, nr 1

203-208

The purpose of this paper is to establish a strong convergence of an implicit iteration process to a common fixed point for a finite family of quasi-contractive operators. Our theorems give an armative response to a question raised by [Xu and Ori, Numer. Funct. Anal. Optim. 22 (2001) 767-773 ].