Taiwanese Journal of Mathematics

ON GENERALIZED VECTOR IMPLICIT VARIATIONAL INEQUALITIES AND COMPLEMENTARITY PROBLEMS

Lu-Chuan Ceng and Sangho Kum

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Abstract

In this paper, two generalized vector implicit variational inequalities and three generalized vector implicit complementarity problems are introduced with a general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions. Furthermore, some existence theorems for the generalized vector implicit variational inequalities are derived by using Lin’s result (1986) and Nadler’s result (1969). We affirmatively answer the open question proposed by Rapcsak (2000). Our results are the extension and improvement of the corresponding results in Huang and Li (2006).

Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 621-636.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404748

Digital Object Identifier
doi:10.11650/twjm/1500404748

Mathematical Reviews number (MathSciNet)
MR2340154

Zentralblatt MATH identifier
1139.49007

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions) 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
ordered Banach space generalized vector implicit variational inequality generalized vector implicit complementarity problem

Citation

Ceng, Lu-Chuan; Kum, Sangho. ON GENERALIZED VECTOR IMPLICIT VARIATIONAL INEQUALITIES AND COMPLEMENTARITY PROBLEMS. Taiwanese J. Math. 11 (2007), no. 3, 621--636. doi:10.11650/twjm/1500404748. https://projecteuclid.org/euclid.twjm/1500404748


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