Abstract
In this article, we consider a generalized multivalued vector variational-like inequality and obtain some existence results. The last result is proved by using the concept of escaping sequences. Some special cases are also discussed.
Similar content being viewed by others
References
Ansari Q.H.: On generalized vector variational-like inequalities. Ann. Sci. Math. Quebec 19, 131–137 (1995)
Border K.C.: Fix point Theorems with Applications to Economics and Game Theory. Cambridge University Press, Cambridge (1985)
Chen G.Y.: Existence of solutions for a vector variational inequality: an extension of Hartman-Stampacchia theorem. J. Optim. Theory Appl. 74, 445–456 (1992)
Chen, G.Y., Chang, G.M.: Vector variational inequalities and vector optimization. Lecture Notes in Economics and Mathematical Systems, 285, Springer-Varlag (1987)
Chen G.Y., Yang X.Q.: Vector complementarity problems and its equivalences with weak minimal element in ordered spaces. J. Math. Anal. Appl. 153, 136–158 (1990)
Chen G.Y., Craven B.D.: A vector variational inequality and optimization over an efficient set. Zeitscrift for Operations Reasearch 3, 1–12 (1990)
Fan K.: A generalization of Tychonoffs fixed point theorem. Math. Anal. 142, 305–310 (1961)
Giannessi F.: Theorems of alternative quadratic programs and complementarity problems. In: Cottle, R., Giannessi, F., Lions, J.L. (eds) Variational Inequalities and Complementarity Problems, Wiley, Chichester (1990)
Giannessi. F.: In: Cottle, R., Giannessi, F., Lions, J.L. (eds.) Vector variational inequality and vector equilibria mathematical theorems. Kluwer Acadamic Publishers, Dordrecht/Boston/London (2000)
Lee G.M., Kim D.S., Lee B.S.: Generalized vector variational inequality. Appl. Math. Lett. 9(1), 39–42 (1996)
Lee G.M., Kim D.S., Lee B.S., Chen G.Y.: Generalized vector variational inequality and its duality and set-valued maps. Appl. Math. Lett. 11(4), 21–26 (1998)
Lee G.M., Kim D.S., Lee B.S., Cho S.J.: Generalized vector variational inequality and fuzzy extention. Appl. Math. Lett. 6, 47–51 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Irfan, S.S., Ahmad, R. Generalized multivalued vector variational-like inequalities. J Glob Optim 46, 25–30 (2010). https://doi.org/10.1007/s10898-009-9404-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9404-4
Keywords
- Generalized multivalued vector variational-like inequality
- Existence result
- Escaping sequence
- Closed graph
- Affine mapping