Abstract
In this paper, the problem of modified iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established.MSC:47H09, 47J05, 47J25, 47H25.
Highlights
Fixed-point theory as an important branch of nonlinear analysis has been applied in the study of nonlinear phenomena
Iterative algorithms for finding common fixed points of nonlinear mappings have been considered by many authors
The well-known convex feasibility problem capture application in various disciplines such as image restorations, and radiation therapy treatment planning is to find a point in the intersection of common fixed-point sets of nonlinear mappings
Summary
Fixed-point theory as an important branch of nonlinear analysis has been applied in the study of nonlinear phenomena. From the method of generating iterative sequence, we can divide iterative algorithms into explicit algorithms Both explicit Mann iterative algorithms and implicit Mann-iterative algorithms have been extensively studied for approximating common fixed points of nonlinear mappings (see [ – ]). We consider the problem of approximating a common fixed point of asymptotically nonexpansive mappings based on a general implicit iterative algorithm, which includes an explicit process as a special case. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [ ] as a generalization of the class of nonexpansive mappings They proved that if C is a nonempty, closed, convex, and bounded subset of a real uniformly convex Banach space, every asymptotically nonexpansive self mapping has a fixed point (see [ ]).
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