A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces

Abstract

In this paper, firstly, we introduce a method for finding common fixed point of $L$ -Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and $L$ -Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness principle for total asymptotically strictly pseudo-non-spreading non-self-mappings is established. Thirdly, the weak convergence theorems of the proposed method to the common fixed point of the above mappings are proved. Our results improved, extended, and generalized some corresponding results in the literature.