The Equivalence Between Two New Iterations And Some New Convergence Theorems

The paper mainly studies the equivalence of some nonlinear iterations and the conver-gence theorems of finite nonexpansive mappings.The paper includes four chapters.The first chapter as an introduction, modeling process of nonlinear iterations and theconvergence theorems of fixed points, its real meaning, the current research status and themain work of this paper are addressed.In the second chapter,it is to establish some groups of equivalent theorems of conver-gence between modified Ishikswa-Halpern iteration and viscosity approximation method.Inthis chapter,it considers the viscosity approximation method with Meir-Keeler contrac-tion(MKC, for short)In the third chapter,we consider the convergence theorems of finite λi strictly pseudo-contractive mappings in Banach space.Finally, the conclusion is showed in the fourth chapter, and some problems we needstudy later are given.