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http://dx.doi.org/10.22771/nfaa.2022.27.04.04

GENERALIZED QUASI-VARIATIONAL-LIKE INEQUALITIES FOR PSEUDO-MONOTONE TYPE II OPERATORS ON NON-COMPACT SETS  

Mohammad S.R., Chowdhury (Department of Mathematics and Statistics, Faculty of Science, The University of Lahore)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.4, 2022 , pp. 743-756 More about this Journal
Abstract
We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.
Keywords
Advanced form of variational-like inequalities; upper hemi-continuous operators; (${\beta}$; g)-pseudo-monotone type II and strong (${\beta}$; g)-pseudo-monotone type II operators; locally convex Hausdorff topological vector spaces;
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1 J.P. Aubin, Applied Functional Analysis, Wiley-Interscience, New York, 1979.
2 J.P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons. Inc., New York, 1984.
3 H. Brezis, L. Nirenberg and G. Stampacchia, A remark on Ky Fan's minimax principle, Boll. U.M.I., 6 (1972), 293-300.
4 Y.J. Cho and H.Y. Lan, A new class of generalized nonlinear multi-valued quasivariational-like-inclusions with H-monotone mappings, Math. Inequal. Appl., 10 (2007), 389-401.
5 M.S.R. Chowdhury, The surjectivity of upper-hemicontinuous and pseudo-monotone type II operators in reflexive Banach Spaces, Ganit: J. Bangladesh Math. Soc., 20 (2000), 45-53.
6 M.S.R. Chowdhury, Generalized variational inequalities for upper hemi-continuous and demi-operators with applications to fixed point theorems in Hilbert spaces, Serdica Math. J., 25 (1998), 163-178.
7 M.S. R. Chowdhury, Afrah A.N. Abdou and Y.J. Cho, Existence theorems of generalized quasi-variational-like inequalities for pseudo-monotone type II operators, J. Inequal. Appl., 449 (2014), 1-18.
8 M.S. R. Chowdhury and Y.J. Cho, Existence theorems of generalized quasi-variationallike inequalities for η-h-pseudo-monotone type I operators on non-compact sets, J. Inequal. Appl., 79 (2012), 1-19.
9 M.S.R. Chowdhury and Y.J. Cho, Generalized bi-quasi-variational inequalities for quasipseudo-monotone type II operators on non-compact sets, J. Inequal. Appl., Article ID 237191, (2010), 1-17.   DOI
10 M.S.R. Chowdhury and K.K. Tan, Generalized variational-like inequalities for pseudomonotone type III operators, Cent. Eur. J. Math., 6 (2008), 526-536.   DOI
11 M.S.R. Chowdhury and K.K. Tan, Application of upper hemi-coninuous operators on generalized bi-quasi-variational inequalities in locally convex topological vector spaces, Positivity, 3 (1999), 333-344.   DOI
12 M.S.R. Chowdhury and K.K. Tan, Applications of pseudo-monotone operators with some kind of upper semi-continuity in generalized quasi-variational inequalities on noncompacts, Proc. Amer. Math. Soc., 126 (1998), 2957-2968.   DOI
13 M.S.R. Chowdhury and K.K. Tan, Generalized variational inequalities for quasimonotone operators and applications, Bull. Polish Acad. Sci., 45 (1997), 25-54.
14 M.S.R. Chowdhury and K.K. Tan, Generalization of Ky Fan's minimax inequality with applications to generalized variational inequalities for pseudo-monotone operators and fixed theorems, J. Math. Anal. Appl., 204 (1996), 910-929.   DOI
15 M.S.R. Chowdhury and G. Tarafdar, Existence theorems of generalized quasi-variational inequalities with upper hemi-continuous and demi-operators on non-compact sets, Math. Inequal. Appl., 2 (1999), 585-597.
16 Y.P. Fang, Y.J. Cho, N.J. Huang and S.M. Kang, Generalized nonlinear implicit quasivariational-like inequalities for set-valued mappings in Banach spaces, Math. Inequal. Appl., 6 (2003), 331-337.
17 M.S.R. Chowdhury and H.B. Thompson, Generalized variational-like inequalities for pseudo-monotone type II operators, Nonlinear Anal., 63 (2005), 321-330.
18 A.P. Ding and G. Tarafdar, Generalized variational-like inequalities with pseudomonotone set-valued mappings, Arch. Math., 74 (2000), 302-313.   DOI
19 K. Fan, A minimax inequality and applications, in "Inequalities, III" , (O. Shisha, Ed.), 103-113, Academic Press, San Diego, 1972.
20 H. Kneser, Sur un theor'eme fundamental de la theorie des jeux, C.R. Acad. Sci. Paris, 234 (1952), 2418-2420.
21 H.Y. Lan, Y.J. Cho and N.J. Huang, Stability of iterative procedures for a class of generalized nonlinear quasi-variational-like inclusions involving maximal η-monotone mappings, Fixed Point Theory and Applications, Edited by Y.J. Cho, J.K. Kim and S.M. Kang, 6 (2006), 107-116.
22 R.T. Rockafeller, Convex Analysis, Princeton Univ. Press, Princeton, 1970.
23 M.H. Shih and K.K. Tan, Generalized bi-quasi-variational inequalities, J. Math. Anal. Appl., 143 (1989), 66-85.   DOI
24 M.H. Shih and K.K. Tan, Generalized quasi-variational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl., 108 (1985), 333-343.   DOI
25 W. Takahashi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan, 28 (1976), 166-181.