We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces. Acknowledgement. The authors A. R. Khan and M. Abbas are grateful to King Fahd University of Petroleum and Minerals for supporting research project IN 121037.

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.

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces. Keywords—Asypmtotically quasi-nonexpansive mappings, Common fixed point, Strong and weak convergence, Iteration process.

We define an iterative process for a finite family of asymptotically quasi-nonexpansive mappings in CAT(0) space and obtain sufficient conditions for the convergence of this iterative scheme to a unique common fixed point of the family. AMS Mathematics Subject Classification (2010): 47H10, 47H09, 54H25

In this paper, we consider the strong convergence of the projection type Ishikawa iteration process to a common fixed point of a finite family of nonself Ii asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Temir and Gul [10], Temir [11], and Thianwan [12].

In this paper, we introduce a new hybrid algorithm of modified Halpern iteration for a countable infinitely family of quasi-φ-nearly asymptotically nonexpansive mappings in Banach spaces and prove the strong convergence for the proposed algorithm. Our proof method is of novelty and the results presented in this paper improve the corresponding ones announced by others. Mathematics Subject Classi...

The purpose of this paper is to study the convergence of a new finite steps iterative sequence with mean errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and generalize some results in the literature.

In this paper, we consider the weak and strong convergence of implicit iteration process to a common fixed point of a finite family of nonself Ii-asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Shazad [8], Temir [5] and Gul [J. Math. Anal. Appl. 329(2007), 759-765]. Mathematics Subject Classification: 47H09, 47J25

Recently, Chang, et al introduce the concept of total asymptotically nonexpansive mapping which contain the asymptotically nonexpansive mapping. The purpose of the paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. Meanwhile, we obtain a ∆-convergence theorem of the three-step iterative scheme for total asymptot...