## Taiwanese Journal of Mathematics

### EXTENDED GENERAL NONLINEAR QUASI-VARIATIONAL INEQUALITIES AND PROJECTION DYNAMICAL SYSTEMS

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 4 (2013), 1321-1352.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706120

Digital Object Identifier
doi:10.11650/tjm.17.2013.2559

Mathematical Reviews number (MathSciNet)
MR3085514

Zentralblatt MATH identifier
1275.49013

#### Citation

Ansari, Qamrul; Balooee, Javad; Yao, Jen-Chih. EXTENDED GENERAL NONLINEAR QUASI-VARIATIONAL INEQUALITIES AND PROJECTION DYNAMICAL SYSTEMS. Taiwanese J. Math. 17 (2013), no. 4, 1321--1352. doi:10.11650/tjm.17.2013.2559. https://projecteuclid.org/euclid.twjm/1499706120

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