Strong convergence by the shrinking effect of two half-spaces and applications

Muhammad Aqeel Ahmad Khan; Hafiz Fukhar-ud-din

doi:10.1186/1687-1812-2013-30

Strong convergence by the shrinking effect of two half-spaces and applications

Muhammad Aqeel Ahmad Khan^*, Hafiz Fukhar-ud-din

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

1 Scopus citations

Abstract

This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature.

Original language	English
Article number	30
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2013
DOIs	https://doi.org/10.1186/1687-1812-2013-30
State	Published - Feb 2013

Bibliographical note

Funding Information:
We wish to thanks the referees for careful reading and helpful comments which led the manuscript to the present form. The author M.A.A. Khan gratefully acknowledges the support from German Science Foundation (DFG Project KO 1737/5-1) and Higher Education Commission of Pakistan. The author H. Fukhar-ud-din is grateful to King Fahd University of Petroleum & Minerals for support during this research.

Keywords

CQ-method
Equilibrium problem
Nonexpansive map
Shrinking projection method
Strict pseudo-contraction
δ-inverse strongly monotone map

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2013-30

Cite this

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title = "Strong convergence by the shrinking effect of two half-spaces and applications",

abstract = "This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature.",

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note = "Funding Information: We wish to thanks the referees for careful reading and helpful comments which led the manuscript to the present form. The author M.A.A. Khan gratefully acknowledges the support from German Science Foundation (DFG Project KO 1737/5-1) and Higher Education Commission of Pakistan. The author H. Fukhar-ud-din is grateful to King Fahd University of Petroleum \& Minerals for support during this research. ",

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N2 - This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature.

AB - This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature.

KW - CQ-method

KW - Equilibrium problem

KW - Nonexpansive map

KW - Shrinking projection method

KW - Strict pseudo-contraction

KW - δ-inverse strongly monotone map

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DO - 10.1186/1687-1812-2013-30

M3 - Article

AN - SCOPUS:84902509447

SN - 1687-1820

VL - 2013

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

M1 - 30

ER -

Strong convergence by the shrinking effect of two half-spaces and applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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