The Convergence Of Iterative Algorithms For Fixed Points Of Asymptotically Quasi Pseudocontractive Type Mappings

In this article, we mainly study the two results. Let E be a strictly convex and uniformly Banach space with the Kadec-Klee. The first result is to introduce an new iterative process which converges strongly to a common element of the set of fixed points of a family of asymptotically strict quasi-Φ-pseudocontractions mappings in the intermediate sense and the solution set of a generalized equilibrium problem in Bananch spaces; it is that we introduce a new generalizedly modified iterative sequence with errors{xn} as follows:where Ti, are asymptotically quasi Φ-nonexppansive mappings;J is a normalized du-ality mapping; The definition of F was introduced;ΠCn+1f is a generalized f-projection operator. We also prove that the iterative sequence{xn} converges strongly to a com-mon element of the set of fixed points of a family of asymptotically strict quasi-Φ-pseudocontractions mappings in the intermediate sense and the solution set of gener-alized equilibrium problem. Modern compared with the existing results, the result is a mainly from the projection operator, iterative method, equilibrium problems, space and nonlinear mapping this five aspects to do the corresponding promotion and improve-ment.The second result is that we introduce a new modified mixed Ishikawa iterative sequence with error{xn} for common fixed points of two class of asymptotically quasi pseudocontractive type nonself mappings in Banach space. Let G is a nonexpansive retract (with P) of E, P is called a nonexpansive retraction mapping. Hi, Kj are two classes of uniformly L—Lipschitzian nonself mappings, Hi is a kind of asymptotically quasi pseudocontractive mapping. Under certain conditions, we prove the sequence{xn} converges strongly to a fixed point of two asymptotically quasi pseu-docontractive type nonself-mappings. The results here extend and improve the corre-sponding results reported by some other authors recently.The structure is that:we introduce some related research backgrounds, concepts and lemmas in the first chapter; in the second chapter, the convergence theorems are given for equilibrium problem and asymptotically strict quasi-Φ-pseudocontractions mappings in the intermediate sense; in the third chapter, we study a new modified mixed Ishikawa iteration for common fixed points of two class of asymptotically quasi pseu-docontractive type nonself mappings in Banach space.