An iterative algorithm for finding a common solution of fixed points and a general system of variational inequalities for two inverse strongly accretive operators

An iterative algorithm for finding a common solution of fixed points and a general system of... In this paper, we introduce an iterative scheme based on a viscosity approximation method with a modified extragradient method for finding a common solutions of a general system of variational inequalities for two inverse-strongly accretive operator and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our results extend and improve the recent results of Qin et al. (J Comput Appl Math 233:231–240, 2009) and many others. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

An iterative algorithm for finding a common solution of fixed points and a general system of variational inequalities for two inverse strongly accretive operators

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0074-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce an iterative scheme based on a viscosity approximation method with a modified extragradient method for finding a common solutions of a general system of variational inequalities for two inverse-strongly accretive operator and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our results extend and improve the recent results of Qin et al. (J Comput Appl Math 233:231–240, 2009) and many others.

Journal

PositivitySpringer Journals

Published: Jul 16, 2010

References

  • Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications
    Qin, X.; Cho, S.Y.; Kang, S.M.

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