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Strong Convergence Theorems for Fixed Point Problems for Nonexpansive Mappings and Zero Point Problems for Accretive Operators Using Viscosity Implicit Midpoint Rules in Banach Spaces

Author

Listed:
  • Huancheng Zhang

    (Qinggong College, North China University of Science and Technology, Tangshan 063000, China)

  • Yunhua Qu

    (Qian’an College, North China University of Science and Technology, Tangshan 064400, China)

  • Yongfu Su

    (Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China)

Abstract

This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results of the proposed algorithm and improves the relevant results of researchers in this field. In the end, this paper gives numerical examples to support the main results.

Suggested Citation

  • Huancheng Zhang & Yunhua Qu & Yongfu Su, 2018. "Strong Convergence Theorems for Fixed Point Problems for Nonexpansive Mappings and Zero Point Problems for Accretive Operators Using Viscosity Implicit Midpoint Rules in Banach Spaces," Mathematics, MDPI, vol. 6(11), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:257-:d:183493
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