A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 33 (2013) no. 1, pp. 41-45.

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In this paper the existence of solutions to variational-type inequalities problems for (η,θ,δ)- pseudomonotone-type set-valued mappings in nonreflexive Banach spaces introduced in [4] is considered. Presented theorem does not require a compact set-valued mapping, but requires a weaker condition 'locally bounded' for the mapping.
Keywords: variational-type inequalities, (η,θ,δ)-pseudomonotone-type, nonreflexive Banach spaces
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Nockowska-Rosiak, Magdalena. A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 33 (2013) no. 1, pp. 41-45. http://geodesic.mathdoc.fr/item/DMDICO_2013_33_1_a2/

[1] S.-S. Chang, B.-S. Lee and Y.-Q. Chen, Variational inequalities for monotone operators in nonreflexive Banach spaces, Appl. Math. Lett. 8 (6) (1995), 29-34. doi: 10.1016/0893-9659(95)00081-Z

[2] K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310. doi: 10.1007/BF01353421

[3] B.-S. Lee and G.-M. Lee, Variational inequalities for (η,θ)-pseudomonotone operators in nonreflexive Banach spaces, Appl. Math. Lett. 12 (5) (1999), 13-17. doi: 10.1016/S0893-9659(99)00050-6

[4] B.-S. Lee, G.-M. Lee and S.-J. Lee, Variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces, Appl. Math. Lett. 15 (1) (2002), 109-114. doi: 10.1016/S0893-9659(01)00101-X

[5] B.-S. Lee and J.-D. Noh, Minty's lemma for (θ,η)-pseudomonotone-type set-valued mappings and applications, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 9 (1) (2002), 47-55.

[6] R.U. Verma, Variational inequalities involving strongly pseudomonotone hemicontinuous mappings in nonreflexive Banach spaces, Appl. Math. Lett. 11 (2) (1998), 41-43. doi: 10.1016/S0893-9659(98)00008-1

[7] P.J. Watson, Variational inequalities in nonreflexive Banach spaces, Appl. Math. Lett. 10 (2) (1997), 45-48. doi: 10.1016/S0893-9659(97)00009-8