## Taiwanese Journal of Mathematics

### SYSTEMS OF GENERALIZED VECTOR QUASI-VARIATIONAL INCLUSION PROBLEMS AND APPLICATION TO MATHEMATICAL

#### Abstract

In this paper, we introduce and study some new systems of generalized vector quasi-variational inclusion problems involving condensing mappings in locally $FC$-uniform spaces. These systems contain many known systems of generalized vector quasi-variational inclusion problems, systems of generalized vector quasi-equilibrium problems and systems of vector quasi-optimization problems as special cases. By applying an existence theorem of maximal elements of a family of set-valued mappings involving condensing mapping due to author, we prove some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems. As applications, some existence results of solutions of the mathematical programs with systems of generalized vector quasi-variational inclusion constraints are established in noncompact locally $FC$-uniform spaces.

#### Article information

Source
Taiwanese J. Math., Volume 13, Number 5 (2009), 1515-1536.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405557

Digital Object Identifier
doi:10.11650/twjm/1500405557

Mathematical Reviews number (MathSciNet)
MR2554474

Zentralblatt MATH identifier
1188.49008

#### Citation

Ding, X. P.; Lai, T. C.; Yu, S. J. SYSTEMS OF GENERALIZED VECTOR QUASI-VARIATIONAL INCLUSION PROBLEMS AND APPLICATION TO MATHEMATICAL. Taiwanese J. Math. 13 (2009), no. 5, 1515--1536. doi:10.11650/twjm/1500405557. https://projecteuclid.org/euclid.twjm/1500405557

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