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2013 EXTENDED GENERAL NONLINEAR QUASI-VARIATIONAL INEQUALITIES AND PROJECTION DYNAMICAL SYSTEMS
Qamrul Ansari, Javad Balooee, Jen-Chih Yao
Taiwanese J. Math. 17(4): 1321-1352 (2013). DOI: 10.11650/tjm.17.2013.2559

Abstract

The aim of this paper is to introduce and study a new class of the extended general nonlinear quasi-variational inequalities and a new class of the extended general Wiener-Hopf equations. The equivalence between the extended general nonlinear quasi-variational inequalities and the fixed point problems, and as well as the extended general Wiener-Hopf equations is established. Then by using these equivalences, we discuss the existence and uniqueness of a solution of the extended general nonlinear quasi-variational inequalities. Applying the equivalent alternative formulation and a nearly uniformly Lipschitzian mapping $S$, we define some new $p$-step projection iterative algorithms with mixed errors for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping $S$ which is also a unique solution of the extended general nonlinear quasi-variational inequalities. The convergence analysis of the suggested iterative schemes under some suitable conditions is studied. We also suggest and analyze a class of extended general projection dynamical systems associated with the extended general nonlinear quasi-variational inequalities. We show that the trajectory of the solution of the extended general projection dynamical system converges globally exponential to a unique solution of the extended general nonlinear quasi-variational inequalities. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

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Qamrul Ansari. Javad Balooee. Jen-Chih Yao. "EXTENDED GENERAL NONLINEAR QUASI-VARIATIONAL INEQUALITIES AND PROJECTION DYNAMICAL SYSTEMS." Taiwanese J. Math. 17 (4) 1321 - 1352, 2013. https://doi.org/10.11650/tjm.17.2013.2559

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1275.49013
MathSciNet: MR3085514
Digital Object Identifier: 10.11650/tjm.17.2013.2559

Subjects:
Primary: 49J40
Secondary: 47H05, 47J20

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 4 • 2013
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