Abstract
AbstractWe show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.
Highlights
Let E, d be a complete metric space and I 0, 1
We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces
If E, d satisfies the conditions of convex structure, E, d is called convex metric space that is denoted as E, d, W
Summary
Let E, d be a complete metric space and I 0, 1. We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces. We will consider a few iteration sequences in convex metric space E, d, W .
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