| Fixed point theorems play a fundamental role in demonstrating the existence of solutionsto a wide variety of problems arising in mathematics, physics, engineering, medicine andsocial science. In this article, we work out strong convergence theorems and weakconvergence theorems for non-expansive mappings on uniformly convex Banach spaces.In chapter1, In order to study the strong convergence theorems of non-expansivemapping, we show some basic conceptions and give the history of strong convergencetheorems history on Banach spaces.In chapter2, we introduce the conception of coupled fixed point and uniformly convexBanach space. At the same time, we study the Mann iterative scheme for a mappingT: X Xon uniformly convex Banach spaces, and get a coupled fixed point of T. Weprove some strong convergence theorems for the Mann iterative scheme involvingquasi-nonexpansive mappings.In chapter3, we discuss the strong convergence theorems of non-expansive non-selfmapping on uniformly convex Banach spaces. Firstly, we study the history of strongconvergence theorems of non-expansive non-self mapping. Secondly, we give a new iterativeschemes and study the strong convergence theorems of two total asymptoticallynon-expansive non-self mappings on Banach spaces, throngh the iterative scheme. In the end,we extend the result of two total asymptotically non-expansive non-self mappings to finitetotal asymptotically non-expansive non-self mappings.In chapter4, we study the fuzzy non-expansive mapping. We try the best to extend thestrong convergence theorems of the common mapping to the fuzzy mapping. The first quarter,we give basic definition and some lemmas. The second quarter, we give the iteration scheme(1.1) and use it to approximate the fixed point and get the strong convergence theorems. Atlast, we extend (1.1) to (1.2), and get more general iterative scheme and result. The thirdquarter, we study the common fixed point of two fuzzy mapping and get the strongconvergence theorems. |
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