바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.19 No.3

Citation Share

GENERALIZED VECTOR MINTY'S LEMMA

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.3, pp.281-288
https://doi.org/10.7468/jksmeb.2012.19.3.281
Lee, Byung-Soo
Lee,, B. (2012). GENERALIZED VECTOR MINTY'S LEMMA. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(3), 281-288, https://doi.org/10.7468/jksmeb.2012.19.3.281

Abstract

In this paper, the author defines a new generalized <TEX>${\eta}$</TEX>, <TEX>${\delta}$</TEX>, <TEX>${\alpha}$</TEX>)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (<TEX>${\eta}$</TEX>, <TEX>${\delta}$</TEX>, <TEX>${\alpha}$</TEX>)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

keywords
Convex cone, Convex mapping, Ordered Banach space, Hausdorff metric, Generalized (<tex> ${\eta}$</tex>, <tex> ${\delta}$</tex>, <tex> ${\alpha}$</tex>)-pseudomonotone, Minty's lemma, Minty-type vector variational-like inequality problem, Stampacchia-type vector variational-like inequality problem

Reference

1.

(2006). Variational-like inequalities with relaxed <TEX>$\eta-\alpha$</TEX> pseudomonotone mappings in Banach spaces. Appl. Math. Lett., 19, 547-554. 10.1016/j.aml.2005.07.010.

2.

Variational and Quasivariational Inequalities, Applications to Free Boundary Problems.

3.

(2008). Regularity results for evolutionary nonlinear variational and quasi- variational inequalities with applicaions to dynamic equilibrium problems. J. Glob. Optim., 40, 29-39. 10.1007/s10898-007-9194-5.

4.

(1990). The vector complementarity problem and its equivalence with the minimal element. J. Math. Anal. Appl., 153, 136-158. 10.1016/0022-247X(90)90270-P.

5.

(2008). Minty's lemma and vector variational-like inequalities. J. Glob. Optim., 40, 463-473. 10.1007/s10898-007-9177-6.

6.

(1997). On connections among separation, penalization and regularization for variational inequalities with point-to-set-operators. Rendiconti del Circolo Matematico di Palermo, Series II, Suppl., 48, 11-18.

7.

On Minty variational principle, In New Trends in Mathematical Programming.

8.

(1996). On some nonlinear elliptic differential functional equations. Acta Math., 115, 271-310.

9.

(2009). Existence of solutions to a generalized system. J. Optim. Theory Appl., 142(2), 355-361. 10.1007/s10957-009-9530-7.

10.

An introduction to Variational Inequalities.

11.

(1999). A vector version of Minty's lemma and application. Appl. Math. Lett., 12, 43-50.

12.

(2002). Variational-type inequalities for (<TEX>$\eta,\theta,\delta$</TEX>)-pseudo-monotone-type set-valued mappings in nonreflexive Banach spaces. Appl. Math. Lett., 15, 109-114. 10.1016/S0893-9659(01)00101-X.

13.

(2000). A vector extension of Bechera and Panda's generalization of Minty's lemma. Indian. J. Pure Appl. Math., 31(11), 1483-1489.

14.

(1998). Existence of solutions for vector optimization problems. J. Math. Anal. Appl., 220, 90-98. 10.1006/jmaa.1997.5821.

15.

(1998). Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Anal. Th. Meth. Appl, 34, 745-765. 10.1016/S0362-546X(97)00578-6.

16.

(2001). On some equilibrium problems for multimaps. J. Comp. Appl. Math., 129, 171-183. 10.1016/S0377-0427(00)00548-3.

17.

(1969). Multi-valued contraction mappings. Pacific J. Math., 30(2), 475-488. 10.2140/pjm.1969.30.475.

18.

Variational Inequalities;Theory and Applications of Monotone Operators.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy