Existence results for generalized vector quasi-equilibrium problems

Tirth Ram; Parshotam Lal

doi:10.26637/MJM0804/0059

Abstract

In this work, we extend Minty’s type lemma for a class of generalized vector quasi-equilibrium problems in Hausdorff topological vector spaces and establish some results on existence of solutions both under compact and noncompact assumption by using 1- person game theorems.

Keywords:

Escaping sequence, upper semicontinuity, hemicontinuous,, P- convex, P- monotone mapping

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Tirth Ram Department of Mathematics, University of Jammu, Jammu- 180006, India. https://orcid.org/0000-0002-6447-6767
Parshotam Lal Department of Mathematics, University of Jammu, Jammu- 180006, India.

Pages: 1675-1680
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

R. Ahmed and M. Akram, Some existence results for generalized vector-quasi equilibrium problems, Bull. Iranian Math. Soc., 41(6)(2015), 1413-1422.

Q.H. Ansari, Vector equilibrium problems and vector variational inequalities, In. F . Gianessi (Ed.) Vector Variational Inequalities and Vector Equilibria:Mathematical Theories, Kluwer Dordrecht(2000), 1-16.

Q.H. Ansari, W. Oettle and D. Schlager, A generalization of vector equilibria, Mathematical Methods of Operational Research, 46(1997), 147-152.

E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Mathematics Student, 63(1994), 123-145.

P. Cubiotti, Existence of solutions for lower semicontinuous quasi-equilibrium problem, Comput. Math. Appl., 30(1995), 11-22.

X.P. Ding, Existence of solutions for quasi-equilibrium problems in noncompact topological spaces, Comput. Math. Appl.,39(2000), 13-21.

X.P. Ding, W.K. Kim and K.K. Tan, Existence of generalized games with L-majorized correspondence,Internat. J. Math. Sci., 17(1994), 783-790.

X.P. Ding, W.K. Kim and K.K. Tan, Equilibria of noncompact generalized game with $mathrm{L}^*$-majorized preference, Journal of Mathematical Analysis and Applications, $164(1992), 508-517$.

K. Fan, A minimax inequality and applications, in $I n$ equalities III, Shisha, Academic Press, (1972), 103-113.

J.Y. Fu, Generalized vector quasi-equilibrium problems, Mathematical Methods of Operational Research, 52(2000), 57-64.

J.Y. Fu, Vector equilibrium problems. Existence theorems and convexity of solution set, Journal of Global Optimization, 31(2005), 109-119.

F. Giannessi, Vector Variational Inequality and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht/ Boston/ London, 2000.

G. Kassay and M. Miholca, Existence results for vector equilibrium problems given by a sum of two functions, Journal of Global Optimization, 63(1)(2015), 195-211.

K.R. Kazmi, On vector equilibrium problem, Proc. Indian Acad. Sci. (Math. Sci.), 110(2)(2000), 213-223.

A. Khaliq and S. Krishan, Vector Quasi-Equilibrium Problems, Bull. Austral. Math. Soc., 68(2003), 295-302.

A. Khaliq and T. Ram, On perturbed implicit vector quasiequilibrium problems, South East Asian Journal of Mathematics and Mathematical Sciences, 7(2008), 63-75.

A. Kristaly and C. Varga, Set-valued version of Ky-Fan's inequality with applications to variational inclusions theory, Journal of Mathematical Analysis and Applications, 282(2003), 8-20.

L. Lin and S. Park, On some generalized quasiequilibrium problems, Journal of Mathematical Analysis and Applications, 224(1998), 167-181.

M.A. Noor and W. Oettli, On general nonlinear complementarity problems and quasi-equilibria, Matematiche, 49(1994), 313-331.

W. Song, Vector equilibrium problems with set-valued mappings, Vector Variational Inequality and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht/ Boston/ London (2000), 403-422.

N.X. Tan and P.N. Tinh, On the existence of equilibrium points of vector functions, Numer. Funct. Anal. Optim., $19(1-2)(1998), 141-156$.

T. Tanaka, Generalized semicontinuity and existence theorems for cone saddle points,Appl. Math. Optim., 36(1997), 313-322.

L. Qun, Generalized vector variational-like inequalities, Nonconvex Optimization and its Applications, F. Giannessi, Editor ( Kluwer Academic Publishers, Dordrecht, 2000), 363-369.