Abstract
Coupled fixed points have become the focus of interest in recent times, especially for their potential applications. Very recently, the idea of common coupled fixed point iterations has been introduced for approximating common coupled fixed points in linear spaces. Here, a coupled Mann pair iterative scheme is defined and is applied to the problem of finding common coupled fixed points of certain mappings. The discussion of the paper is in the context of Hilbert spaces.
Highlights
One of the most attractive research topics in fixed point theory is to prove the existence of a fixed point on metric spaces endowed with partial orders [1,2]
Let F : C × C → C be any mapping defined on a closed nonempty convex subset C of a Hilbert space H such that F satisfies Condition A
Our purpose in this paper is to introduce a new algorithm which is called the coupled Mann pair iterative scheme for arriving at a common coupled fixed point for certain mappings
Summary
One of the most attractive research topics in fixed point theory is to prove the existence of a fixed point on metric spaces endowed with partial orders [1,2]. For any nonempty set X and a mapping F : X × X → X, ( x, y) ∈ X × X is said to be a coupled fixed point of F, if
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