Existence of Solutions for Generalized Quasi-Variational Like Inequalities

Ding Xieping

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(2): 131-139

Ding Xieping. Existence of Solutions for Generalized Quasi-Variational Like Inequalities[J]. Applied Mathematics and Mechanics, 1997, 18(2): 131-139.

Citation:

Ding Xieping. Existence of Solutions for Generalized Quasi-Variational Like Inequalities[J]. Applied Mathematics and Mechanics, 1997, 18(2): 131-139.

Citation:

Ding Xieping. Existence of Solutions for Generalized Quasi-Variational Like Inequalities[J]. Applied Mathematics and Mechanics, 1997, 18(2): 131-139.

PDF( 599 KB)

Existence of Solutions for Generalized Quasi-Variational Like Inequalities

Ding Xieping

Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China

Received Date: 1995-11-10
Publish Date: 1997-02-15

Abstract

Abstract

In this paper, some existence theorems of solutions for a class of generalizedquasi-variational-like inequalities with discontinuous mappings are proved underparacompact setting in topological vector spaces. These theorems unify, improve andgeneralize many recent results.
- topological vector space,
- generalized quasi-variational-like inequality,
- 0-diagonally concave,
- 0-diagonally concave relation

FullText(HTML)

References(25)

References

[1]	J.P,Aubin and I.Ekeland,Applied Nonlinear Analtlsis,John Wiley&Sons,New York (1984).
[2]	C.Baiocchi and A,Capelo,Variational and Quasivariational Inequalities,John Wiley & Sons,New York (1984).
[3]	D,Kinderlehrer and G,Stampacchi,An Introduction to Irariational Inequalities,Acad.Press,New York (1980).
[4]	D.Chan and J,S.Pang,The generalized quasi-variational inequalities,Math,Oiler,Res.,(1982),211-222.
[5]	P,T,Harker and J.S,Pang,Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory,algorithms and applications,Math,Program,Ser,B,4(1990),161-220.
[6]	M,A,Noor,General variational inequalities,Appl,Math,Lett.,1 (1988),119-122.
[7]	M.A,Noor,G eneral algorithm an d sensitivity for variational inequalities,J.Appl.Math,Stoch,Anal,,(1992),2 9-42.
[8]	M,A,Noor,K,I,Noor and T,M,Rassias,So me aspects of variational inequalities,J.Comput,Appl.Math,,47(1993),285-312.
[9]	J.C,Yao,General variational.inequalities in B anach spaces,Appl.Moth,Lett.,5(1) (1992),51-54.
[10]	J.C,Yao,On the general variational inequalities,J.Math,Ana.Appl.,174(1993),550-555.
[11]	J,C.Yao and J.S.Guo,Variational and generalized variational inequalities with discontinuous mappings,J.Math,Anal.Appl.,182(1994),371-392.
[12]	X,P,Ding and E,Tarafdar,Generalized nonlinear variational inequalities with non-m onotone set-valued mappings,Appl,Math,Lett.7(4) (1994),5-11.
[13]	丁协平,一类广义变分不等式及应用,四川师范大学学报,17(6)(1994),10-16.
[14]	丁协平,一类广义变分不等式解的存在性,烟台大学学报,2 (1995),15-22.
[15]	丁协平,具有间断映象的隐变分不等式,四川师范大学学报,18(2)(1995),8-15
[16]	J.Parida,M.Sahoo and A,Kumar,A variational-like inequality problem,BuI!.Austral.Math,Soc.,3(1989),225-231.
[17]	N,H,Dien,Some remarks on variational-like inequalities,Bull,Austral.Math,Soc,,4(1992),335-342.
[18]	A,H,Siddiqi,A,Khaliq and Q.H,Ansari,On variational-like inequalities,Ann,Sci,Quebec,18(1) (1994),95-104.
[19]	丁协平,拟变分不等式和社会平衡,应用数学和力学,12(7) (1991),599-606.
[20]	20 W,W,Hogan,Point-to-set maps in mathematical programming,SIAM Rev,,1(1973),591-603.
[21]	M,H,Shih and K.K,Tan,Covering theorems of convex sets related fixed pint theorems,in Nonlinear and Convex Andhsis,Marcel Dekker Incc.New York(1987),235-244.
[22]	J,X,Zhou and G.Chen,Diiagonzl convexity conditions for problems in convex analysis and quasi-variational inequalities,J.Math,Anal.Appl.,132 (1988),213-225.
[23]	H.Kneser,Suruti théoéme; fondamantal de la théorie des jeux,C,R,Acad,Sci,Paris,23(1952),2418-2420.
[24]	J,C.Yao,Generalized-quasi-vzriational inequality problems with discontinuous mappings,Math,Opera.Res,,20(2) (1005),965-478.
[25]	O,H,Merrill,Applications and extcr.sions of an algorithm that computes fixed points of certrain upper semi-continuous point-to-set mappings,Ph.D,Thesis,Univ,of Michigan,Ann Arbor,MI,(1972).