An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

Adrian Petruşel; Jen-Chih Yao

Open Mathematics (2009)

  • Volume: 7, Issue: 2, page 335-347
  • ISSN: 2391-5455

Abstract

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In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.

How to cite

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Adrian Petruşel, and Jen-Chih Yao. "An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems." Open Mathematics 7.2 (2009): 335-347. <http://eudml.org/doc/269555>.

@article{AdrianPetruşel2009,
abstract = {In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.},
author = {Adrian Petruşel, Jen-Chih Yao},
journal = {Open Mathematics},
keywords = {Modified extragradient method; Viscosity approximation method; Fixed point; α-inverse-strongly-monotone mapping; Nonexpansive mapping; Variational inequalities; modified extragradient method; viscosity approximation method; fixed point; -inverse-strongly-monotone mapping; nonexpansive mapping; variational inequalities},
language = {eng},
number = {2},
pages = {335-347},
title = {An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems},
url = {http://eudml.org/doc/269555},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Adrian Petruşel
AU - Jen-Chih Yao
TI - An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems
JO - Open Mathematics
PY - 2009
VL - 7
IS - 2
SP - 335
EP - 347
AB - In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
LA - eng
KW - Modified extragradient method; Viscosity approximation method; Fixed point; α-inverse-strongly-monotone mapping; Nonexpansive mapping; Variational inequalities; modified extragradient method; viscosity approximation method; fixed point; -inverse-strongly-monotone mapping; nonexpansive mapping; variational inequalities
UR - http://eudml.org/doc/269555
ER -

References

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