Variable KM-like algorithms for fixed point problems and split feasibility problems

Abdul Latif; Daya R. Sahu; Qamrul H. Ansari

doi:10.1186/1687-1812-2014-211

Variable KM-like algorithms for fixed point problems and split feasibility problems

Abdul Latif^*, Daya R. Sahu, Qamrul H. Ansari

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

15 Scopus citations

Abstract

The convergence analysis of a variable KM-like method for approximating common fixed points of a possibly infinitely countable family of nonexpansive mappings in a Hilbert space is proposed and proved to be strongly convergent to a common fixed point of a family of nonexpansive mappings. Our variable KM-like technique is applied to solve the split feasibility problem and the multiple-sets split feasibility problem. Especially, the minimum norm solutions of the split feasibility problem and the multiple-sets split feasibility problem are derived. Our results can be viewed as an improvement and refinement of the previously known results. MSC:47H10, 65J20, 65J22, 65J25.

Original language	English
Article number	211
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1186/1687-1812-2014-211
State	Published - 18 Dec 2014

Bibliographical note

Publisher Copyright:
© 2014, Latif et al.; licensee Springer.

Keywords

convergence analysis of algorithms
fixed point problems
regularized algorithms
split feasibility problems

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2014-211

Cite this

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abstract = "The convergence analysis of a variable KM-like method for approximating common fixed points of a possibly infinitely countable family of nonexpansive mappings in a Hilbert space is proposed and proved to be strongly convergent to a common fixed point of a family of nonexpansive mappings. Our variable KM-like technique is applied to solve the split feasibility problem and the multiple-sets split feasibility problem. Especially, the minimum norm solutions of the split feasibility problem and the multiple-sets split feasibility problem are derived. Our results can be viewed as an improvement and refinement of the previously known results. MSC:47H10, 65J20, 65J22, 65J25.",

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AU - Latif, Abdul

AU - Sahu, Daya R.

AU - Ansari, Qamrul H.

PY - 2014/12/18

Y1 - 2014/12/18

N2 - The convergence analysis of a variable KM-like method for approximating common fixed points of a possibly infinitely countable family of nonexpansive mappings in a Hilbert space is proposed and proved to be strongly convergent to a common fixed point of a family of nonexpansive mappings. Our variable KM-like technique is applied to solve the split feasibility problem and the multiple-sets split feasibility problem. Especially, the minimum norm solutions of the split feasibility problem and the multiple-sets split feasibility problem are derived. Our results can be viewed as an improvement and refinement of the previously known results. MSC:47H10, 65J20, 65J22, 65J25.

AB - The convergence analysis of a variable KM-like method for approximating common fixed points of a possibly infinitely countable family of nonexpansive mappings in a Hilbert space is proposed and proved to be strongly convergent to a common fixed point of a family of nonexpansive mappings. Our variable KM-like technique is applied to solve the split feasibility problem and the multiple-sets split feasibility problem. Especially, the minimum norm solutions of the split feasibility problem and the multiple-sets split feasibility problem are derived. Our results can be viewed as an improvement and refinement of the previously known results. MSC:47H10, 65J20, 65J22, 65J25.

KW - convergence analysis of algorithms

KW - fixed point problems

KW - regularized algorithms

KW - split feasibility problems

UR - https://www.scopus.com/pages/publications/84924177045

U2 - 10.1186/1687-1812-2014-211

DO - 10.1186/1687-1812-2014-211

M3 - Article

AN - SCOPUS:84924177045

SN - 1687-1820

VL - 2014

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

M1 - 211

ER -

Variable KM-like algorithms for fixed point problems and split feasibility problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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