Strong and weak convergence of Ishikawa iterations for best proximity pairs
| Autor: | A. Anthony Eldred, Moosa Gabeleh, S. I. Ezhil Manna, Olivier Olela Otafudu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
47h09
uniformly convex banach space noncyclic relatively nonexpansive mapping 021103 operations research Weak convergence General Mathematics 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology Topology 01 natural sciences 46b20 best proximity pair ishikawa iteration QA1-939 0101 mathematics Geometry and topology 47h10 Mathematics |
| Zdroj: | Open Mathematics, Vol 18, Iss 1, Pp 10-21 (2020) |
| ISSN: | 2391-5455 |
| Popis: | Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be a noncyclic relatively nonexpansive mapping if T(A) ⊆ A, T(B) ⊆ B and ∥Tx − Ty∥ ≤ ∥x − y∥ for all (x, y) ∈ A × B. A best proximity pair for such a mapping T is a point (p, q) ∈ A × B such that p = Tp, q = Tq and d(p, q) = dist(A, B). In this work, we introduce a geometric notion of proximal Opiaľs condition on a nonempty, closed and convex pair of subsets of strictly convex Banach spaces. By using this geometric notion, we study the strong and weak convergence of the Ishikawa iterative scheme for noncyclic relatively nonexpansive mappings in uniformly convex Banach spaces. We also establish a best proximity pair theorem for noncyclic contraction type mappings in the setting of strictly convex Banach spaces. |
| Databáze: | OpenAIRE |
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