Iterative Approximation Of Fixed Point Of A Finite Family Of Asymptotically Quasi-nonexpansive Mappings

In this paper, the Convergence theorems of iteration sequences are discussed in Banach space and CAT(O) space. This paper contains four parts as following:In chapter one, we will discuss the backgrounds of fixed point theories, main contents and significance of study in this paper.In chapter two, the purpose of this article is to introduce a finite family of asymptotically quasi-nonexpansive mappings in a uniformly convex Banach space. Under certain conditions, we study a multi-step Ishikawa-type iteration sequence and prove that the sequence strongly converges to a common fixed point of the finite family of asymptotically quasi-nonexpansive mappings.In chapter three, a iteration sequence of two finite families of asymptotically nonexpansive mappings is introduced, which is generalized the multi-step Ishikawa-type iteration sequence. Under certain conditions, the weak and strong convergence theorems are proved in Banach space.In chapter four, this paper introduce a finite family of total asymptotically nonexpansive mappings in CAT(O) spaces. Under certain conditions, we study a multi-mixed Agarwal-O’ Regan-Sahu type iterative scheme and prove that the se-quence Δ and strongly converges to the two finite families of total asymptotically nonexpansive mappings. Our results generalize and unify many important known results of many others.