Abstract
Abstract In this paper, we show that convergence of Picard, Mann, Krasnoselskij and Ishikawa iterations is equivalent in cone normed spaces. Also, we prove that semistability of these iterations is equivalent.
Highlights
Let (E, · E) be a real Banach space
A subset P ⊆ E is called a cone in E if it satisfies the following conditions: (i) P is closed, nonempty and P = { }, (ii) a, b ∈ R, a, b ≥ and x, y ∈ P imply that ax + by ∈ P, (iii) x ∈ P and –x ∈ P imply that x =
The space E can be partially ordered by the cone P, by defining x ≤ y if and only if y – x ∈ P
Summary
Let (E, · E) be a real Banach space. A subset P ⊆ E is called a cone in E if it satisfies the following conditions:(i) P is closed, nonempty and P = { }, (ii) a, b ∈ R, a, b ≥ and x, y ∈ P imply that ax + by ∈ P, (iii) x ∈ P and –x ∈ P imply that x =. ([ ]) Let (X, dc) be a cone metric space, P be a normal cone and {Tn}n∈N be a sequence of self-maps of X with n F(Tn) = ∅. Let X be a cone Banach space, P be a normal cone and T be a Zamfirescu self-map of X.
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