An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings

Alongkot Suvarnamani; Mongkol Tatong

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 1, page 45-59
  • ISSN: 0044-8753

Abstract

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We introduce an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of paper we utilize our results to study the zeros of the maximal monotone and some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., [Math. Meth. Oper. Res., 67:375–390, 2008] and many others.

How to cite

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Suvarnamani, Alongkot, and Tatong, Mongkol. "An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings." Archivum Mathematicum 048.1 (2012): 45-59. <http://eudml.org/doc/246866>.

@article{Suvarnamani2012,
abstract = {We introduce an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of paper we utilize our results to study the zeros of the maximal monotone and some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., [Math. Meth. Oper. Res., 67:375–390, 2008] and many others.},
author = {Suvarnamani, Alongkot, Tatong, Mongkol},
journal = {Archivum Mathematicum},
keywords = {nonexpansive mapping; fixed point problems; Variational inequality; relaxed extragradient approximation method; maximal monotone; nonexpansive mapping; fixed point problem; variational inequality; relaxed extragradient approximation method},
language = {eng},
number = {1},
pages = {45-59},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings},
url = {http://eudml.org/doc/246866},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Suvarnamani, Alongkot
AU - Tatong, Mongkol
TI - An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 1
SP - 45
EP - 59
AB - We introduce an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of paper we utilize our results to study the zeros of the maximal monotone and some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., [Math. Meth. Oper. Res., 67:375–390, 2008] and many others.
LA - eng
KW - nonexpansive mapping; fixed point problems; Variational inequality; relaxed extragradient approximation method; maximal monotone; nonexpansive mapping; fixed point problem; variational inequality; relaxed extragradient approximation method
UR - http://eudml.org/doc/246866
ER -

References

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