Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 11, Number 3 (2007), 621-636.
ON GENERALIZED VECTOR IMPLICIT VARIATIONAL INEQUALITIES AND COMPLEMENTARITY PROBLEMS
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).
Taiwanese J. Math., Volume 11, Number 3 (2007), 621-636.
First available in Project Euclid: 18 July 2017
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Zentralblatt MATH identifier
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
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