Skip to main content
Log in

A random fixed point iteration for three random operators on uniformly convex Banach spaces

  • Published:
Analysis in Theory and Applications

Abstract

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The results is also an extension of a known theorem in the corresponding non-random case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chang, S.S. and Tan, K.K., Iteration Processes for Approximating Fixed Points of Operators of Monotone Type, Bull. Austral. Math. Soc., 57(1998), 433–445.

    MATH  MathSciNet  Google Scholar 

  2. Chidume, C.E. and Osilike, M.O., Ishikawa Iteration Process for Nonlinear Lipschitz Strongly Accretive Mappings, J. Math. Anal. Appl., 192(1995), 727–741.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chidume, C.E. and Moore, C., Fixed Point Iteration for Pseudocontractive Maps, Proc. Amer. Math. Soc., 127(1999), 1163–1170.

    Article  MATH  MathSciNet  Google Scholar 

  4. Choudhury, B.S., Convergence of a Random Iteration Scheme to a Random Fixed Point, J. Appl. Math. Stoc. Anal., 8(1995), 139–142.

    Article  MATH  MathSciNet  Google Scholar 

  5. Choudhury, B.S. and Ray, M., Convergence of an Iteration Leading to a Solution of Random Operator Equation, J. Appl. Math. Stoc. Anal., 12(1999), 161–168.

    Article  MATH  MathSciNet  Google Scholar 

  6. Choudhury, B.S. and Upadhyay, A., An Iteration Leading of Random Solutions and Fixed Points of Operators, Soochow J. Math., 25(1999), 395–400.

    MATH  MathSciNet  Google Scholar 

  7. Dotson, W.G. Jr. On the Mann Iterative Process, Trans. Amer. Math. Soc., 149(1970), 65–73.

    Article  MATH  MathSciNet  Google Scholar 

  8. Himmelberg, C.J., Measurable Ralations. Fund Math.. LXXXVII(1975), 53–71.

    MathSciNet  Google Scholar 

  9. Ishikawa, S., Fixed Points by a New Iteration Method, Proc. Amer, Math. Soc., 44(1974), 147–150.

    Article  MATH  MathSciNet  Google Scholar 

  10. Maiti, M. and Ghosh, M.K., Approximating Fixed Points by Ishikawa Iterates, Bull. Austral. Math. Soc., 40(1989), 113–117.

    Article  MATH  MathSciNet  Google Scholar 

  11. Senter, H.F. and Dotson, W.G. Jr., Approximating Fixed Points of Non-Expensive Mappings, Proc. Amer. Math. Soc., 44(1974), 375–380.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Choudhury, B.S. A random fixed point iteration for three random operators on uniformly convex Banach spaces. Anal. Theory Appl. 19, 99–107 (2003). https://doi.org/10.1007/BF02835233

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02835233

Key Words

AMS (2000) subject classification

Navigation