45
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Random Nonlinear Variational Inequalities for Mappings of Monotone Type in Banach Spaces

&
Pages 489-499 | Accepted 16 Jan 2004, Published online: 15 Feb 2007

REFERENCES

  • Bharucha-Reid , A. T. 1972 . Random Integral Equations . Academic Press .
  • Binh , T. Q. , and N. M. Chuong . 1996 . On a fixed point theorem . Functional Analysis and Its Applications 30 : 220 – 221 . [CSA]
  • Binh , T. Q. , and N. M. Chuong . 1999 . On a fixed point theorem for nonexpansive nonlinear operator . Acta Mathematica Vietnamica 24 : 1 – 8 . [CSA]
  • Binh , T. Q. , and N. M. Chuong . 2001 . Approximation of nonlinear operator equations . Numer. Funct. Anal. Optim. 22 ( 7–8 ): 831 – 844 . [CSA] [CROSSREF] [CROSSREF]
  • Breris , H. , M. G. Crandall , and A. Pazy . 1970 . Perturbations of nonlinear maximal monotone sets in Banach spaces . CPAM 23 : 123 – 144 . [CSA]
  • Browder , F. E. 1966 . Problèmes Nonlinéaires . Montreal : Press de I' Université de Montreal .
  • Browder , F. E. 1968 . Semicontractive and semiaccretive nonlinear mappings in Banach spaces . Bull. Amer. Math. Soc. 74 : 660 – 665 . [CSA]
  • Browder , F. E. 1968 . Nonlinear maximal monotone operators in Banach spaces . Math. Anal. 175 : 89 – 113 . [CSA] [CROSSREF] [CROSSREF]
  • Browder , F. E. , and P. Hess . 1972 . Nonlinear mapping of monotone type in Banach spaces . Functional Anal. 11 : 251 – 294 . [CSA] [CROSSREF] [CROSSREF]
  • Chuong , N. M. , Ya. Mamedov , and K. V. Ninh . 1992 . Approximate Solution of Operator Equations . Hanoi : Sci. & Techn. Publishing House .
  • Chuong , N. M. , and K. V. Ninh . 1991 . On approximative normal values of multivalued operators in vector topological spaces . J. Izv. Vuzov SSSR 12 : 89 . [CSA]
  • Chuong , N. M. , and N. X. Thuan . 2001 . Random fixed point theorems for multivalued nonlinear mapping . Random. Oper. and Stoch. Equa. 9 ( 3 ): 345 – 355 . [CSA]
  • Chuong , N. M. , and N. X. Thuan . 2001 . Nonlinear variational inequalities for random weakly semimonotone operators . Random. Oper. and Stoch. Equa. 9 ( 4 ): 1 – 10 . [CSA]
  • Chuong , N. M. , and N. V. Kinh . 1991 . Regularization of variational inequalities with perturbed non-monotone and discontinuous operators . Differentialnye Uravneniya 27 ( 12 ): 1271 – 1272 . [CSA]
  • Chuong , N. M. , and N. X. Thuan . 2002 . The surjectivity of semiregular maximal monotone random mappings . Random Oper and Stoch. Equa. 10 ( 1 ): 13 – 24 . [CSA]
  • Chuong , N. M. , and N. X. Thuan . 2002. Random equations for weakly semimonotone operator of type (S) and semi J-monotone operator of type (J.S). Random Oper. and Stoch. Equa. 16:123–132. [CSA]
  • Chuong , N. M. , and N. X. Thuan . 2002 . Random equations for semi-H-monotone operators . Rand. Oper. and Stocha. Equa. 10 ( 4 ): 1 – 8 . [CSA]
  • Himmelberg , C. J. 1975 . Measurable relations . Fund. Math. 87 : 53 – 72 . [CSA]
  • Itoh , S. 1978 . Nonlinear random equations with monotone operators in Banach spaces . Math. Anal. 236 : 133 – 146 . [CSA] [CROSSREF] [CROSSREF]
  • Kannan , R. , and H. Salehi . 1977 . Random nonlinear equations and monotonic nonlinearities . J. of Math. Anal. and Appl. 57 : 234 – 256 . [CSA] [CROSSREF] [CROSSREF]
  • Kato , T. 1964 . Demicontinuity, hemicontinuity and monotonicity . Bull. Amer. Math. Soc. 6 : 548 – 550 . [CSA]
  • Kuratowski , K. , and C. Ryll-Nardzewski . 1965 . A general theorem on selectors . Bull. Acad. Sci. Math. Astronom. Physics 13 : 397 – 403 . [CSA]
  • Kravvaritis , D. 1988 . Nonlinear random operators of monotone type in Banach space . J. Math. Anal. Appl. 78 : 488 – 496 . [CSA] [CROSSREF] [CROSSREF]
  • Lim , T.-C. 1974 . A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space . Bull. AMS 80 : 1123 – 1126 . [CSA]
  • Lin , T.-C. 1995 . Random approximation and random fixed point theorems for continuous 1-set contractive random maps . In Proc. AMS 123 : 1167 – 1176 . [CSA]
  • Nga , N. Q. , N. M. Chuong . 2001 . On a set valued nonlinear variational inequality . Differentialnye Uravneniya 37 ( 1 ): 1 – 2 . [CSA]
  • Nga , N. Q. , and N. M. Chuong . 1999 . Some fixed point theorems for non-compact and weakly asymptotically regular set-valued mappings. Preprint 99/38, Institute of Math., NCST, Numer. Funct. Anal. and Optim ( accepted ). [CSA]
  • Nga , N. Q. 2002 . Set-valued nonlinear variational inequalities for H-monotone mappings in nonreflexive Banach spaces . Nonliear Analysis, TMA, Series A: TMA 52 : 457 – 465 . [CSA]
  • Thuan , N. X. 2000 . Random solution to the equations T(ω, u(ω), u(ω)) = b(ω) and applications to nonlinear elliptic boundary value problems . Preprint 2000/39, Institute of Mathematics, submitted to Vietnam Jour. of Math. [CSA]
  • Vainberg , M. 1972 . The Variational Method and the Method of Monotone Operators . Moscow : Nauka .
  • Xu , H.-K. 1993 . A random fixed point theorem for multivalued nonexpansive operators in uniformly comvex Banach spaces . In Proc. AMS 117 ( 4 ): 1989 – 1992 . [CSA]
  • Zeidler , E. 1986 . Nonlinear Functional Analysis and its Apptications . I, IB, II.B . New York : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.