Abstract
In this paper, we introduce a new concept of W-nonexpansive mappings and obtain fixed point theorems for nonexpansive mappings for non-convex set. Our results resolve fixed pointed problem that nonexpansive mappings be not on closed convex set, and it extends fixed point theorems for nonexpansive mappings.
Highlights
Obtained fixed points theorem for nonexpansive mapping
Introduction and preliminariesFixed point theory is widely applied in engineering
Definition 1.2 Let (X, d) be a metric space and T: X → X be a given mapping, if there exists a function W: X X → 0, ∞) such that W(x, y)d(Tx, Ty) ≤ d(x, y), ∀x, y ∈ X, we say that T is a W-nonexpansive mapping
Summary
Obtained fixed points theorem for nonexpansive mapping. Definition 1.1 Let X be a nonempty set, the function W: X X → 0, ∞) is called triangular if for all x, y ∈ X, if W(x, y) ≥ 1, W(y, z) ≥ 1 or W(y, x) ≥ 1, W(y, z) ≥ 1, W(x, z) ≥ 1. Definition 1.2 Let (X, d) be a metric space and T: X → X be a given mapping, if there exists a function W: X X → 0, ∞) such that W(x, y)d(Tx, Ty) ≤ d(x, y), ∀x, y ∈ X, we say that T is a W-nonexpansive mapping.
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