The Convergence Theorems For Fixed Points Of Nonlinear Operators In Banach Spaces

The fixed point theory of nonlinear operations are important parts of nonlinear func-tional analysis. Especially, the problem of approximating to solutions of nonlinear operator equations becomes the topic that people study in the recently years. In this paper, we intro-duce effective schemes with asymptotically quasi-φ-nonexpansive mappings, nonexpansive semigroup and strictly pseudocontractive mappings. Results presented in this paper improve and extend many authors’recent results. This paper includes five chapters. Now we will describe them briefly one by one.The first chapter as an introduction, Introducing the history and present situation of nonlinear operator equations in Banach spaces and we also give a summary of this work.In the second chapter, we introduce a general iterative algorithm for finding a com-mon element of the set of common fixed points of infinite family of asymptotically quasi-φ-nonexpansive mappings and of the set of solutions for finite equilibrium problems in a real Banach space.In the third chapter, we study the implicit and explicit viscosity iteration schemes for nonexpansive semigroup in a reflexive, strictly convex and uniformly smooth Banach space which satisfies Opial’s condition.In the forth chapter, we study an iteration schemes for fixed point problems of a count-able family of strictly pseudocontractive mappings in q-uniformly smooth Banach spaces.Finally, the conclusion is showed in the fifth chapter.