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GENERALIZED VECTOR MINTY'S LEMMA

이병수
한국수학교육학회|2012.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제19권 제3호|pp. 281-288|DOI http://dx.doi.org/

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참고문헌

키워드

Hausdorff metricOrdered Banach spaceConvex coneConvex mappingGeneralized (ηδα)-pseudomonotoneMinty's lemma
주제분류수학

초록

In this paper, the author de¯nes a new generalized (η,δ , α)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (´; ±; ®)-pseudomonotone mappings in Banach spaces, called the gener-alized vector Minty's lemma.

Abstract

In this paper, the author de¯nes a new generalized (η,δ , α)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (´; ±; ®)-pseudomonotone mappings in Banach spaces, called the gener-alized vector Minty's lemma.

참고문헌 (18)

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  11. B.-S. Lee, "A vector version of Minty's lemma and application", Appl. Math. Lett, 12, pp.43~50 (1999)
  12. B.-S. Lee, "Variational-type inequalities for (n,θ,δ)-pseudo-monotone-type set-valued mappings in nonreflexive Banach spaces", Appl. Math. Lett, 15, pp.109~114 (2002)
  13. B.-S. Lee, "A vector extension of Bechera and Panda's generalization of Minty's lemma", Indian. J. Pure Appl. Math, 31(11), pp.1483~1489 (2000)
  14. G.M. Lee, "Existence of solutions for vector optimization problems", J. Math. Anal. Appl, 220, pp.90~98 (1998)
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  18. G. Stampacchia, "Variational Inequalities, In Theory and Applica- tions of Monotone Operators", Proc. NATO ADV. Study Institute, Venice, pp.101~192 (1969)

관련 논문AI추천

MINTY'S LEMMA FOR STRONG IMPLICIT VECTOR VARIATIONAL INEQUALITY SYSTEMS김승현, 이병수한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제4호VECTOR F-COMPLEMENTARITY PROBLEMS WITH g-DEMI-PSEUDOMONOTONE MAPPINGS IN BANACH SPACES이병수, M. Firdosh Khan, Salahuddin영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호Generalized variational-like inequalities with compositely monotone multifunctions이규명, Jen-Chih Yao, Lu-Chuan Ceng대한수학회 · 대한수학회지2008 · 제45권 제3호SCALARIZATION METHODS FOR MINTY-TYPE VECTOR VARIATIONAL INEQUALITIES이병수영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호GENERALIZED F-IMPLICIT MULTIVALUED VARIATIONAL INEQUALITY PROBLEMS AND COMPLEMENTARITY PROBLEMS이병수, M. Firdosh Khan, Salahuddin영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES WITH CORRESPONDING NON-SMOOTH VECTOR OPTIMIZATION PROBLEMS이병수한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제2호

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