In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767–77...

The purpose of this paper is to propose an algorithm for solving the split common fixed point problems for total asymptotically strictly pseudocontractive mappings in infinite-dimensional Hilbert spaces. The results presented in the paper improve and extend some recent results of Moudafi 2011 and 2010 , Xu 2010 and 2006 , Censor and Segal 2009 , Censor et al. 2005 , Masad and Reich 2007 , Censo...

In this paper, we introduce iterative algorithms for finding a common element of the set of fixed points for an asymptotically strict pseudocontractive mappings in the intermediate sense, the set of solutions of the variational inequalities for a family of α-inverse-strongly monotone mappings and the set of solutions of a system of equilibrium problems in a Hilbert space. We establish some weak...

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...

In this article, we introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to solution common The results proved extend improve recent Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, Qin, Appl. Math. Comput., \(\bf 219\) (20...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...