Generalized variational-like inequalities with compositely monotone multifunctions
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we introduce two classes of generalized variational- like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η-α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed η-α semimonotone multifunctions in arbitrary Banach spaces by virtue of the Kakutani-Fan- Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.
Abstract
In this paper, we introduce two classes of generalized variational- like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η-α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed η-α semimonotone multifunctions in arbitrary Banach spaces by virtue of the Kakutani-Fan- Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.
참고문헌 (21)
- O. Chadli, "On generalized vector pre-variational and prequasivariational inequalities", Journal of Mathematical Analysis and Applications, 295(2), pp.392~403 (2004)
- S. S. Chang, "Variational inequalities for monotone operators in nonreflexive Banach spaces", Applied Mathematics Letters, 8(6), pp.29~34 (1995)
- Y. Q. Chen, "On the semi-monotone operator theory and applications", Journal of Mathematical Analysis and Applications, 231(1), pp.177~192 (1999)
- R. W. Cottle, "Pseudo-monotone complementarity problems in Hilbert space", Journal Optimization Theory & Applications, 75(2), pp.281~295 (1992)
- K. Fan, "Some properties of convex sets related to fixed point theorems", Mathematische Annalen, 266(4), pp.519~537 (1984)
- Y. P. Fang, "Variational-like inequalities with generalized monotone mappings in Banach spaces", Journal Optimization Theory & Applications, 118(2), pp.327~338 (2003)
- F. Giannessi, "Vector Variational Inequalities and Vector Equilibria" (2000), Kluwer Academic Publishers
- D. Goeleven, "Eigenvalue and dynamic problems for variational and hemivariational inequalities", Communications on Applied Nonlinear Analysis, 3(4), pp.1~21 (1996)
- N. Hadjisavvas, "Quasimonotone variational inequalities in Banach spaces", Journal Optimization Theory & Applications, 90(1), pp.95~111 (1996)
- P. Hartman, "On some non-linear elliptic differential-functional equations", Acta Mathematica, 115, pp.271~310 (1966)
- I. V. Konnov, "On the generalized vector variational inequality problem", Journal of Mathematical Analysis and Applications, 206(1), pp.42~58 (1997)
- S. B. Jr. Nadler, "Multi-valued contraction mappings", Pacific Journal of Mathematics, 30, pp.475~488 (1969)
- A. H. Siddiqi, "On nonlinear variational inequalities", Indian Journal of Pure and Applied Mathematics, 25(9), pp.969~973 (1994)
- R. U. Verma, "Nonlinear variational inequalities on convex subsets of Banach spaces", Applied Mathematics Letters, 10(4), pp.25~27 (1997)
- R. U. Verma, "On monotone nonlinear variational inequality problems", COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 39(1), pp.91~98 (1998)
- X. Q. Yang, "A class of nonconvex functions and pre-variational inequalities", Journal of Mathematical Analysis and Applications, 169(2), pp.359~373 (1992)
- J. C. Yao, "Existence of generalized variational inequalities", Operations Research Letters, 15(1), pp.35~40 (1994)
- G. X. Z. Yuan, "KKM Theory and Applications in Nonlinear Analysis, Monographs and Textbooks in Pure and Applied Mathematics", pp.218~ (1999), Marcel Dekker, Inc.
- L. C. Zeng, "Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities", Computers & Mathematics with Applications, 50(5), pp.935~945 (2005)
- L. C. Zeng, "Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities", Journal Optimization Theory & Applications, 124(3), pp.725~738 (2005)
- L. C. Zeng, "Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces", Journal of Global Optimization, 36(4), pp.483~497 (2006)