On the equivalence between some kinds of implicit and explicit iterations with applications

Shih Sen Chang; Jong Kyu Kim; Heung Wing Joseph Lee; Chi Kin Chan

doi:10.1186/1687-1812-2012-55

On the equivalence between some kinds of implicit and explicit iterations with applications

Shih Sen Chang, Jong Kyu Kim, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

The purpose of this article is to study the equivalence between some kinds of implicit and explicit iterative approximations. As applications, we utilize our results to study the approximation problems arising in nonexpansive semigroup, variationa inclusions and equilibrium problem.

Original language	English
Article number	55
Journal	Fixed Point Theory and Applications
Volume	2012
DOIs	https://doi.org/10.1186/1687-1812-2012-55
Publication status	Published - 1 Dec 2012

Keywords

Browder's property
Fixed point
Halpern's property
Moudafi's viscosity approximation
Nonexpansive mapping
Reich's convergence theorem
Suzuki's type strong convergence theorem
Weak contractive mapping
Xu's convergence theorem

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

More information

10.1186/1687-1812-2012-55

http://hdl.handle.net/10397/6571

Cite this

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title = "On the equivalence between some kinds of implicit and explicit iterations with applications",

abstract = "The purpose of this article is to study the equivalence between some kinds of implicit and explicit iterative approximations. As applications, we utilize our results to study the approximation problems arising in nonexpansive semigroup, variationa inclusions and equilibrium problem.",

keywords = "Browder's property, Fixed point, Halpern's property, Moudafi's viscosity approximation, Nonexpansive mapping, Reich's convergence theorem, Suzuki's type strong convergence theorem, Weak contractive mapping, Xu's convergence theorem",

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AU - Kim, Jong Kyu

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AU - Chan, Chi Kin

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AB - The purpose of this article is to study the equivalence between some kinds of implicit and explicit iterative approximations. As applications, we utilize our results to study the approximation problems arising in nonexpansive semigroup, variationa inclusions and equilibrium problem.

KW - Browder's property

KW - Fixed point

KW - Halpern's property

KW - Moudafi's viscosity approximation

KW - Nonexpansive mapping

KW - Reich's convergence theorem

KW - Suzuki's type strong convergence theorem

KW - Weak contractive mapping

KW - Xu's convergence theorem

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DO - 10.1186/1687-1812-2012-55

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JF - Fixed Point Theory and Applications

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ER -

On the equivalence between some kinds of implicit and explicit iterations with applications

Abstract

Keywords

ASJC Scopus subject areas

More information

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