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Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications

Author

Listed:
  • Lili Chen

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
    Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China)

  • Ni Yang

    (Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China)

  • Jing Zhou

    (School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China)

Abstract

In this paper, we first propose the concepts of ( ζ , η , λ , π ) -generalized hybrid multi-valued mappings, the set of all the common attractive points ( C A f , g ) and the set of all the common strongly attractive points ( C s A f , g ), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets A f , F f and C A f , g for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two ( ζ , η , λ , π ) -generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two ( ζ , η , λ , π ) -generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.

Suggested Citation

  • Lili Chen & Ni Yang & Jing Zhou, 2020. "Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1307-:d:395481
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    References listed on IDEAS

    as
    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
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