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A Mean Convergence Theorem without Convexity for Finite Commutative Nonlinear Mappings in Reflexive Banach Spaces

Author

Listed:
  • Lawal Yusuf Haruna

    (Department of Mathematical Sciences, Kaduna State University, Kaduna P.M.B. 2339, Nigeria
    These authors contributed equally to this work.)

  • Bashir Ali

    (Department of Mathematical Sciences, Bayero University, Kano 700006, Nigeria
    These authors contributed equally to this work.)

  • Yekini Shehu

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
    These authors contributed equally to this work.)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
    These authors contributed equally to this work.)

Abstract

This paper investigates the Bregman version of the Takahashi-type generic 2-generalized nonspreading mapping which includes the generic 2-generalized Bregman nonspreading mapping as a special case. Relative to the attractive points of nonlinear mapping, the Baillon-type nonlinear mean convergence theorem for finite commutative generic 2-generalized Bregman nonspreading mappings without the convexity assumption is proved in the setting of reflexive Banach spaces. Using this result, some new and well-known nonlinear mean convergence theorems for the finite generic generalized Bregman nonspreading mapping, the 2-generalized Bregman nonspreading mapping and the normally 2-generalized hybrid mapping, among others, are established. Our results extend and generalize many corresponding ones announced in the literature.

Suggested Citation

  • Lawal Yusuf Haruna & Bashir Ali & Yekini Shehu & Jen-Chih Yao, 2022. "A Mean Convergence Theorem without Convexity for Finite Commutative Nonlinear Mappings in Reflexive Banach Spaces," Mathematics, MDPI, vol. 10(10), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1678-:d:815105
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