Abstract
A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in (1).
Highlights
Introduction and PreliminariesIt is desiralble to add the convex structure in [3, 6] to cone metric spaces and consider an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings in convex cone metric spaces.Throughout this paper, E is a normed vector space with a normal solid cone P .Definition 1.1. [2] A nonempty subset P of E is called a cone if P is closed, P= {θ}, for a, b ∈ R+ = [0, ∞) and x, y ∈ P, ax + by ∈ P and P ∩ {−P } = {θ}
We define a partial ordering ≼ in E as x ≼ y if y − x ∈ P . x
The least positive number k is called the normal constant of P
Summary
It is desiralble to add the convex structure in [3, 6] to cone metric spaces and consider an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings in convex cone metric spaces. [5] Let (X, d) be a cone metric space and T : (X, d) → (X, d) a mapping. Is said to be asymptotically nonexpansive if there exists a sequence such that lim n→∞
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