Abstract
AbstractThis work is devoted to analyzing the feasibility study of a Moudafi viscosity projection method with a weak contraction for a finite family of quasinonexpansive mappings in a Hadamard space. To this end, we need to construct a countable family of nonexpansive mappings satisfying AKTT condition with a weak contraction by choosing an appropriate control sequence under certain conditions.
Highlights
Let C be a nonempty subset of a metric space (X, d)
The well-known Banach contraction principle is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain selfmappings of metric spaces
One generalization of the contraction principle for weak contractions is obtained by Alber and Guerre-Delabriere [ ] in Hilbert spaces
Summary
Let C be a nonempty subset of a metric space (X, d). Suppose that, for each x ∈ X, there exists a unique point PCx ∈ C such that d(x, PCx) = d(x, C) = infy∈C d(x, y). It is known that the fixed point set of a quasinonexpansive mapping defined on a CAT( ) space (see Section for the definition) is closed and convex. Approximation methods for finding specific fixed points of a family of nonexpansive mappings in Hilbert, Banach, and geodesic metric spaces have been studied by many researchers; see, e.g., [ – ] and the references therein. Let us denote by F(T) the common fixed point set of all mappings in a family T For solving a common fixed point problem for a finite family of quasinonexpansive mappings in a geodesic metric space is still open. The purpose of this paper is to analyze the feasibility study of Moudafi viscosity type of projection method with a weak contraction for a finite family of quasinonexpansive mappings in a complete CAT( ) space, known as a Hadamard space.
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