A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces

Magdalena Nockowska-Rosiak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

  • Volume: 33, Issue: 1, page 41-45
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Magdalena Nockowska-Rosiak. "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 33.1 (2013): 41-45. <http://eudml.org/doc/270215>.

@article{MagdalenaNockowska2013,
abstract = {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.},
author = {Magdalena Nockowska-Rosiak},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {variational-type inequalities; (η,θ,δ)-pseudomonotone-type; nonreflexive Banach spaces; -pseudomonotone-type set-valued mappings},
language = {eng},
number = {1},
pages = {41-45},
title = {A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces},
url = {http://eudml.org/doc/270215},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Magdalena Nockowska-Rosiak
TI - A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 1
SP - 41
EP - 45
AB - 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.
LA - eng
KW - variational-type inequalities; (η,θ,δ)-pseudomonotone-type; nonreflexive Banach spaces; -pseudomonotone-type set-valued mappings
UR - http://eudml.org/doc/270215
ER -

References

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  1. [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 Zbl0840.47052
  2. [2] K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310. doi: 10.1007/BF01353421 Zbl0093.36701
  3. [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 Zbl0954.47052
  4. [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 Zbl1032.47043
  5. [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. [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 Zbl06587015
  7. [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 Zbl0907.49003

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