Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 6
192
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Generalized random linear operators on a Hilbert space

&
Pages 1040-1059 | Received 07 Jul 2011, Accepted 12 Sep 2012, Published online: 04 Dec 2012

References

  • Diestel , J. and Uhl , J.J. 1977 . Vector Measures , Providence, RI : AMS .
  • Dorogovstev , A.A. 1986 . On application of Gaussian random operator to random elements . Teor. Veroyatnost. Primenen. , 30 : 812 – 814 .
  • Dunford , N. and Schwarts , J.T. 1963 . Linear Operator Part II , New York : Interscience Publishers .
  • Engl , H.W. , Nashed , M.Z. and Zuhair , M. 1981 . Generalized inverses of random linear operators in Banach spaces . J. Math. Anal. Appl. , 83 ( 2 ) : 582 – 610 .
  • Nashed , M.Z. and Engl , H.W. 1979 . “ Random generalized inverses and approximate solution of random equations ” . In Approximate Solution of Random Equations , Edited by: Bharucha-Reid , A.T. 149 – 210 . New York/Amsterdam : Elsevier/North-Holland .
  • Nualard , D. and Pardoux , E. 1988 . Stochastic calculus with anticipating integral . Prob. Theory Relat. Fields , 78 : 535 – 581 .
  • Shahzad , N. 2004 . Random fixed points of K-set- and pseudo-contractive random maps . Nonlinear Anal. , 57 ( 2 ) : 173 – 181 .
  • Shahzad , N. 2004 . Random fixed points of pseudo-contractive random operators . J. Math. Anal. Appl. , 296 ( 1 ) : 302 – 308 .
  • Shahzad , N. 2008 . Random fixed point results for continuous pseudo-contractive random maps . Ind. J. Math. , 50 ( 2 ) : 263 – 271 .
  • Shahzad , N. and Hussain , N. 2006 . Deterministic and random coincidence point results for f-nonexpansive maps . J. Math. Anal. Appl. , 323 : 1038 – 1046 .
  • Skorokhod , A.V. 1984 . Random Linear Operators , Dordrecht : Reidel Publishing Company .
  • Sunder , V.S. 1998 . Functional Analysis: Spectral Theory , Boston/Berlin : Birkhauser Verlag .
  • Tan , K.K. and Yuan , X.Z. 1993 . On deterministic and random fixed points . Proc. Amer. Math. Soc. , 119 : 849 – 856 .
  • Thang , D.H. 1995 . The adjoint and the composition of random operators on a Hilbert space . Stochas. Int. J. Prob. Stochas. Process. , 54 : 53 – 73 . (formerly Stochastic and Stochastic Reports)
  • Thang , D.H. 1998 . Series and spectral representations of random stable mappings . Stochas. Int. J. Prob. Stochas. Process. , 64 : 33 – 49 . (formerly Stochastic and Stochastic Reports)
  • Thang , D.H. 2008 . Transforming random operators into random bounded operators . Random Oper. Stochastic Equations , 16 : 293 – 302 .
  • Thang , D.H. and Anh , T.N. 2010 . On random equations and applications to random fixed point theorems . Random Oper. Stochastic Equations , 18 : 199 – 212 .
  • Thang , D.H. and Cuong , T.M. 2009 . Some procedures for extending random operators . Random Oper. Stochastic Equations , 17 : 359 – 380 .
  • Thang , D.H. and Thinh , N. 2004 . Random bounded operators and their extension . Kyushu J. Math. , 58 : 257 – 276 .
  • Verma , R.U. 1997 . Stochastic approximation-solvability of linear random equations involving numerical ranges . J. Appl. Math. Stoch. Anal. , 10 : 47 – 55 .

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.