In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

in this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. the results generalise the results of several authors in literature including xiang [chang he xiang, fixed point theorem for generalized $phi$-pseudocontra...

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...

We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi’s hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is pr...

the purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. the results in this paper improve and extend the corresponding results of xu and ori, zhou and chang, sun, yang and yu in some aspects.

Abstract The aim of this paper to present some weak and strong convergence results for countable family non-self mappings. More precisely, we employ the Mann–Dotson’s algorithm approximate common fixed points a k -strict Pseudocontractive mappings in q -uniformly smooth Banach spaces.

In this paper, we propose a modified implicit iteration for two finite families of asymptotically pseudocontractive mappings. Further, convergence theorems for approximation of common fixed points of two finite families of uniformly Lipschitzian asymptotically pseudocontractive mappings are proved in Banach spaces. Our results extend and improve a number of results in the literature. We also re...

CONVERGENCE ANALYSIS OF AN ITERATION SCHEME FOR LIPSCHITZ STRONGLY PSEUDOCONTRACTIVE MAPPINGS Shin Min Kang Department of Mathematics, Gyeongsang National University, Jinju 660-701, KOREA [email protected] Arif Rafiq Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan [email protected] ABSTRACT In this paper, we establish the strong convergence for the Agarwal et al. [1] ite...

In this paper, strong convergence theorems of Ishikawa type implicit iteration process with errors for a finite family of asymptotically nonexpansive in the intermediate sense and asymptotically quasi-pseudocontractive type mappings in normed linear spaces are established by using a new analytical method, which essentially improve and extend some recent results obtained by Yang [Convergence the...

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...