Modified Generalized Ishikawa Iterative Approximations Of The Common Fixed Points For Asymptotically Pseudo-contractive Type Mappings

The fixed point theory is an important part of nonlinear functional analysis. S-ince the Banach contraction mapping theorem was proved by Banach, more and more scholars study these from space, mappings and iterative structure, and got a lot of beneficial theorems results.In this thesis, we deal with the strong convergence the-orems of three-step modified Iterative approximation with errors for asymptotically pseudo-contractive mapping, the strong convergence for asymptotically quasi pseudo-contractive type nonself-mappings and the iterative approximation problems for the finite families of generalized asymptotically nonexpansive nonself-maps.In the first chapter, we introduce some related research background, some relevant knowledge and some related lemmas.In the second chapter, we give a new modified three-step iterative sequence with errors.Without the condition of the sequence is bounded, we prove that the sequence converges strongly to a fixed points of an uniformly Lipschitziza asymptotically pseudo-contractive mapping.We also point out the necessary condition of the strong conver-gence for the iterative sequence.In the third chapter, by using the new modified Ishikawa iterative sequence with error, under suitable conditions, the strong convergence theorems for asymptotically quasi pseudo-contractive tape nonself-mappings is proved.In the fourth chapter, in an arbitrary real Banach space, a new modified generalized Ishikawa iterative sequence with error is introduced for two finite families of general-ized asymptotically nonexpansive nonself-mappings with the intermediate sense, and under suitable conditions, we prove that the iterative sequence converges strongly to a common fixed point of the two finite families of the maps in the chapter.