Abstract
AbstractIn this paper, we consider a split equality fixed point problem for quasi-pseudo-contractive mappings which includes split feasibility problem, split equality problem, split fixed point problem etc., as special cases. A unified framework for the study of this kind of problems and operators is provided. The results presented in the paper extend and improve many recent results.
Highlights
Let C and Q be nonempty closed and convex subsets of the real Hilbert spaces H and H, respectively
Denote by the solution set of split equality fixed point problem ( . )
Throughout this section, we assume that H, H, and H are three real Hilbert spaces
Summary
Let C and Q be nonempty closed and convex subsets of the real Hilbert spaces H and H , respectively. Moudafi [ – ] introduced the following split equality feasibility problem (SEFP): to find x ∈ C, y ∈ Q such that Ax = By, where A : H → H and B : H → H are two bounded linear operators. In order to avoid using the projection, recently, Moudafi [ ] introduced and studied the following problem: Let T : H → H and S : H → H be nonlinear operators such that Fix(T) = ∅ and Fix(S) = ∅, where Fix(T) and Fix(S) denote the sets of fixed points of T and S, respectively. Denote by the solution set of split equality fixed point problem We note that the class of demicontractive mappings is fundamental; it includes many kinds of nonlinear mappings such as the directed mappings, the quasi-nonexpansive mappings, and the strictly pseudo-contractive mappings with fixed points as special cases.
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