On the strong and △-convergence of nsp-iteration on CAT(0) spaces

Piyanan Pasom; Asawathep Cuntavepanit

On the strong and △-convergence of nsp-iteration on CAT(0) spaces

Interdisciplinary Studies Academic Group

Mahidol University

Research output: Contribution to journal › Article › peer-review

Abstract

Let C be a nonempty closed convex subset of a complete CAT(0) space X. We define a modified NSP-iteration for a nonexpansive selfmapping T on C as follows: x₁ ∈ C, and for each n ∈ ℕ, (formula presented)The strong and △-convergence of the above iteration scheme under some certain conditions of the sequences {a_n}, {b_n}, {c_n}, {α_n} and {β_n} in [0, 1] are shown. Our results extend and generalize many results in the literature.

Original language	English
Pages (from-to)	341-351
Number of pages	11
Journal	Thai Journal of Mathematics
Volume	14
Issue number	2
Publication status	Published - Aug 2016

Keywords

CAT(0) spaces
NSP-iteration
Nonexpansive mappings
Strong convergence
△-convergence

Cite this

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abstract = "Let C be a nonempty closed convex subset of a complete CAT(0) space X. We define a modified NSP-iteration for a nonexpansive selfmapping T on C as follows: x1 ∈ C, and for each n ∈ ℕ, (formula presented)The strong and △-convergence of the above iteration scheme under some certain conditions of the sequences \{an\}, \{bn\}, \{cn\}, \{αn\} and \{βn\} in [0, 1] are shown. Our results extend and generalize many results in the literature.",

keywords = "CAT(0) spaces, NSP-iteration, Nonexpansive mappings, Strong convergence, △-convergence",

author = "Piyanan Pasom and Asawathep Cuntavepanit",

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language = "English",

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T1 - On the strong and △-convergence of nsp-iteration on CAT(0) spaces

AU - Pasom, Piyanan

AU - Cuntavepanit, Asawathep

PY - 2016/8

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N2 - Let C be a nonempty closed convex subset of a complete CAT(0) space X. We define a modified NSP-iteration for a nonexpansive selfmapping T on C as follows: x1 ∈ C, and for each n ∈ ℕ, (formula presented)The strong and △-convergence of the above iteration scheme under some certain conditions of the sequences {an}, {bn}, {cn}, {αn} and {βn} in [0, 1] are shown. Our results extend and generalize many results in the literature.

AB - Let C be a nonempty closed convex subset of a complete CAT(0) space X. We define a modified NSP-iteration for a nonexpansive selfmapping T on C as follows: x1 ∈ C, and for each n ∈ ℕ, (formula presented)The strong and △-convergence of the above iteration scheme under some certain conditions of the sequences {an}, {bn}, {cn}, {αn} and {βn} in [0, 1] are shown. Our results extend and generalize many results in the literature.

KW - CAT(0) spaces

KW - NSP-iteration

KW - Nonexpansive mappings

KW - Strong convergence

KW - △-convergence

UR - https://www.scopus.com/pages/publications/84985906568

M3 - Article

AN - SCOPUS:84985906568

SN - 1686-0209

VL - 14

SP - 341

EP - 351

JO - Thai Journal of Mathematics

JF - Thai Journal of Mathematics

IS - 2

ER -

On the strong and △-convergence of nsp-iteration on CAT(0) spaces

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