Study On The Theory Of Fixed Points In β-normed Linear Space

This paper mainly sdudies the properties of theories of fixed points inβ-normed linear space,There are four chapters in this paper.In the Introduction section of the paper,we start from the preliminary and some basic theorems and results.we also introduce some conceptions and notations which will appear in the following chapters.In chapter 1, We study the problem of iterative approximations of fixed points ofφ-strongly pseudo-contractive mapping inβ-normed linear space,the modified Mann iterations with errors are introduced, we prove that the Mann iterative provesses with errors ofφ-strongly pseudo-contractive mapping have strong con-vergence to the fixes point inβ-normed linear space.In chapter 2, we discuss the problem of iterative approximations of fixed points of total asymptotically nonexpansive mappings inβ-normed linear space,under certain conditions, we prove that the Ishikawa iterative provesses with errors of total asymptotically nonexpansive mappings have convergence.In chapter 3, we study the problem of iterative approximations of fixed points of generalized asymptotically quasi-nonexpansive mappings inβ-normed linear space.In chapter 4, we make a conclusion of our work, and point out some problems needed to be solved.