In this paper, a new mixed type iteration process for approximating common fixed point of two asymptotically nonexpansive self-mappings and nonself-mappings is constructed. We then establish strong convergence theorem under mild conditions in uniformly convex hyperbolic space. The results presented here extend improve some related the literature.

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

in this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex banach space. we establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and satisfying solutions of the split feasibility problem (SFP) and systems of equilibrium problem (SEP) in Hilbert spaces. We prove that the sequence generated by the proposed algorithm converge strongly to a common elem...

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 nonexpan...

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...

Four recent papers 1–4 present simple and elegant proofs of fixed point results for pointwise contractions, asymptotic pointwise contractions, and asymptotic nonexpansive mappings. Kirk and Xu 1 study these mappings in the context of weakly compact convex subsets of Banach spaces, respectively, in uniformly convex Banach spaces. Hussain and Khamsi 2 consider these problems in the framework of m...

In 1974, Lim 1 developed a result concerning the existence of fixed points for multivalued nonexpansive self-mappings in uniformly convex Banach spaces. This result was extended to nonself-mappings satisfying the inwardness condition independently by Downing and Kirk 2 and Reich 3 . This result was extended to weak inward mappings independently by Lim 4 and Xu 5 . Recently, Dhompongsa et al. 6 ...

This paper is concerned with an ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces.

In this paper, we introduce a class of total quasi-φ-asymptotically nonexpansive nonself mappings which contain several kinds of mappings as its special cases, and obtain some strong convergence theorems for this type of mappings in Banach spaces under some mild control conditions. The results presented in this paper improve and extend some recent corresponding results.