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An Iterative Method for a Class of Generalized Global Dynamical System Involving Fuzzy Mappings in Hilbert Spaces

  • Yun-zhi Zou
  • Xin-kun Wu
  • Wen-bin Zhang
  • Chang-yin Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7666)

Abstract

This paper presents a class of generalized global dynamical system involving (H,η) set-valued monotone mappings and a set-valued function induced by a closed fuzzy mapping in Hilbert spaces. By using the resolvent operator technique and Nadler fixed-point theorem, we prove the equilibrium point set is not empty and closed. Furthermore, we develop a new iterative scheme which generates a Cauchy sequence strongly converging to an equilibrium point.

Keywords

Generalized dynamical system Variational inequality equilibrium Fuzzy mapping Iterative method Resolvent operator 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yun-zhi Zou
    • 1
  • Xin-kun Wu
    • 2
  • Wen-bin Zhang
    • 3
  • Chang-yin Sun
    • 1
  1. 1.School of AutomationSoutheast UniversityNanjingP.R. China
  2. 2.College of MathematicsSichuan UniversityChengduP.R. China
  3. 3.College of Statistics and MathematicsYunnan University of Finance and EconomicsKunmingP.R. China

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