Abstract
Abstract In this paper, an implicit iterative algorithm with errors is considered for two families of generalized asymptotically nonexpansive mappings. Strong and weak convergence theorems of common fixed points are established based on the implicit iterative algorithm. Mathematics Subject Classification (2000) 47H09 · 47H10 · 47J25
Highlights
In nonlinear analysis theory, due to applications to complex real-world problems, a growing number of mathematical models are built up by introducing constraints which can be expressed as subproblems of a more general problem
The well-known convex feasibility problem which captures applications in various disciplines such as image restoration, computer tomography, and radiation therapy treatment planning is to find a point in the intersection of common fixed point sets of a family of nonexpansive mappings, see, for example, [3,4,5]
It is known that T enjoys a unique fixed point, and the sequence generated in Picard iterative algorithm can converge to the unique fixed point
Summary
Due to applications to complex real-world problems, a growing number of mathematical models are built up by introducing constraints which can be expressed as subproblems of a more general problem. It is known that if C is a nonempty bounded closed convex subset of a uniformly convex Banach space E, every asymptotically nonexpansive mapping on C has a fixed point.
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