On monotone nonlinear variational inequality problems

Ram U. Verma

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 91-98
  • ISSN: 0010-2628

Abstract

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The solvability of a class of monotone nonlinear variational inequality problems in a reflexive Banach space setting is presented.

How to cite

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Verma, Ram U.. "On monotone nonlinear variational inequality problems." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 91-98. <http://eudml.org/doc/248241>.

@article{Verma1998,
abstract = {The solvability of a class of monotone nonlinear variational inequality problems in a reflexive Banach space setting is presented.},
author = {Verma, Ram U.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear varionational inequality problems; $p$-monotone and $p$-Lipschitzian operators; KKM mappings; nonlinear variational inequality problems; -monotone operators; -Lipschitzian operators; KKM mappings},
language = {eng},
number = {1},
pages = {91-98},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On monotone nonlinear variational inequality problems},
url = {http://eudml.org/doc/248241},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Verma, Ram U.
TI - On monotone nonlinear variational inequality problems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 91
EP - 98
AB - The solvability of a class of monotone nonlinear variational inequality problems in a reflexive Banach space setting is presented.
LA - eng
KW - nonlinear varionational inequality problems; $p$-monotone and $p$-Lipschitzian operators; KKM mappings; nonlinear variational inequality problems; -monotone operators; -Lipschitzian operators; KKM mappings
UR - http://eudml.org/doc/248241
ER -

References

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  1. Browder F.E., On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 419-425. (1966) Zbl0143.36902MR0203533
  2. Browder F.E., Petryshyn W.V., Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl. 20 (1967), 197-228. (1967) MR0217658
  3. Fan K., Some properties of convex sets related to fixed point theorems, Math. Annal. 266 (1984), 519-537. (1984) Zbl0515.47029MR0735533
  4. Glowinski R., Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York, 1984. Zbl1139.65050MR0737005
  5. Goeleven D., Motreanu D., Eigenvalue and dynamic problems for variational and hemivariational inequalities, Comm. Appl. Nonlinear Anal. 3 (4) (1996), 1-21. (1996) Zbl0911.49009MR1420282
  6. Noor M.A., Mixed variational inequalities, Appl. Math. Lett. 3 (1990), 73-75. (1990) Zbl0714.49014MR1052253
  7. Noor M.A., General auxiliary principle for variational inequalities, PanAmerican Math. J. 4 (1) (1994), 27-44. (1994) Zbl0845.49005MR1259947
  8. Siddiqi A.H., Ansari Q.H., Kazmi K.R., On nonlinear variational inequalities, Indian J. Pure Appl. Math. 25 (9) (1994), 969-973. (1994) MR1294066
  9. Szulkin A., Positive solutions of variational inequalities: A degree-theoretic approach, J. Diff. Equ. 57 (1985), 90-111. (1985) Zbl0535.35029MR0788424
  10. Verma R.U., Iterative algorithms for variational inequalities and associated nonlinear equations involving relaxed Lipschitz operators, Appl. Math. Lett. 9 (4) (1996), 61-63. (1996) Zbl0864.65039MR1415453
  11. Verma R.U., Generalized variational inequalities involving multivalued relaxed monotone operators, Appl. Math. Lett., to appear. Zbl0960.49509MR1458162
  12. Verma R.U., Nonlinear variational and constrained hemi-variational inequalities involving relaxed operators, Z. Angew. Math. Mech. 77 (1997), 387-391. (1997) MR1455359
  13. Yao J.-C., Applications of variational inequalities to nonlinear analysis, Appl. Math. Lett. 4 (1991), 89-92. (1991) Zbl0734.49003
  14. Zeidler E., Nonlinear Functional Analysis and its Applications IV, Springer-Verlag, New York, 1988. Zbl0648.47036MR0932255

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