• Title/Summary/Keyword: Bregman projection

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A PARALLEL ITERATIVE METHOD FOR A FINITE FAMILY OF BREGMAN STRONGLY NONEXPANSIVE MAPPINGS IN REFLEXIVE BANACH SPACES

  • Kim, Jong Kyu;Tuyen, Truong Minh
    • Journal of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.617-640
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    • 2020
  • In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

A NEW ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEM AND FINDING COMMON FIXED POINTS OF BREGMAN STRONGLY NONEXPANSIVE MAPPINGS

  • Biranvand, Nader;Darvish, Vahid
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.777-798
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    • 2018
  • In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

Strong Convergence of a Bregman Projection Method for the Solution of Pseudomonotone Equilibrium Problems in Banach Spaces

  • Olawale Kazeem Oyewole;Lateef Olakunle Jolaoso;Kazeem Olalekan Aremu
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.69-94
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    • 2024
  • In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.