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Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

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  • Mohammed Ali Alghamdi
  • Naseer Shahzad
  • Habtu Zegeye

Abstract

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Suggested Citation

  • Mohammed Ali Alghamdi & Naseer Shahzad & Habtu Zegeye, 2014. "Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, July.
    • Handle: RePEc:hin:jnljam:580686
    DOI: 10.1155/2014/580686
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    Cited by:

    1. Simeon Reich & Truong Minh Tuyen, 2020. "Two Projection Algorithms for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 148-168, July.

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