The purpose of this paper is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The method of the proof is different from the original one. Our results improve and extend the corresponding results announced by Zhou et al. 2010, Kimura and Takahashi 2009, and some others.

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.

and Applied Analysis 3 (b) η-strongly monotone if there exists a constant η > 0 such that ⟨Sx − Sy, x − y⟩ ≥ η 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 2 , ∀x, y ∈ C; (12) (c) α-inverse-strongly monotone (α-ism) if there exists a constant α > 0 such that ⟨Sx − Sy, x − y⟩ ≥ α 󵄩󵄩󵄩󵄩Sx − Sy 󵄩󵄩󵄩󵄩 2 , ∀x, y ∈ C. (13) Obviously, if S is α-inverse-strongly monotone, then it is monotone and (1/α)-Lipschitz continuous. It can be ...

Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...

In this paper, an iterative scheme for finding common solutions of the set fixed points a pair asymptotically quasi-nonexpansive mapping and minimizers minimization problem is constructed. Using idea jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on space or operator. Our improve, extend generalize many important in literature.

In this paper, we propose and analyze an explicit type algorithm for finding a common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two countable families of total quasi-φ-asymptotically nonexpansive mappings in a Banach space E. As an application of our result, we suggest a framework for finding a common solution of...

Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings....

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.