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Perturbed Iterative Approximation of Common Fixed Points on Nonlinear Fuzzy and Crisp Mixed Family Operator Equation Couples in Menger PN-Spaces

  • Heng-you Lan
  • Tian-xiu Lu
  • Huang-lin Zeng
  • Xiao-hong Ren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)

Abstract

In this paper, based on the concept of probabilistic (ϕ,ψ)-contractor couple introduced by Mihet, a new class of nonlinear operator equation couples with a mixed family of fuzzy and crisp operator equations in Menger probabilistic normed spaces (briefly, Menger PN-spaces) is introduced and studied. Further, some new iterative algorithms are constructed, and the existence of solutions for the nonlinear operator equation couples and the convergence of iterative sequences generated by the algorithms under a larger class of t-norms and joint orbitally complete conditions are discussed.

Keywords

Common fixed point probabilistic (ϕ and ψ)-contractor nonlinear fuzzy and crisp mixed family operator equation couple joint orbitally complete condition iterative algorithm and convergence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Heng-you Lan
    • 1
  • Tian-xiu Lu
    • 1
  • Huang-lin Zeng
    • 2
  • Xiao-hong Ren
    • 2
  1. 1.Department of MathematicsSichuan University of Science & EngineeringZigong, SichuanPeople’s Republic of China
  2. 2.School of Automation and Electronic InformationSichuan University of Science & EngineeringZigong, SichuanP.R. China

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