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EXISTENCE RESULTS FOR NEW GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES
Olawale Kazeem Oyewole,Oluwatosin Temitope Mewomo 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
In this paper, existence and uniqueness results for the solution of a new classof equilibrium problem is established. Using the KKM technique, we establish the existenceand uniqueness of solutions of a new generalized mixed equilibrium problem (NGMEP) withtrifunctions. Further, we propose an iterative algorithm for finding a common element inthe solution set of the NGMEP and a fixed point set of a nonlinear mapping. We provedthe strong convergence of the algorithm to a common element in the solution set of a systemof NGMEP and a fixed point set of a countable family of totally quasi-φ-asymptoticallynonexpansive mapping in the framework of a real uniformly convex and uniformly smoothBanach space. Our result generalize many other results obtained recently in this direction.
Olawale Kazeem Oyewole,Lateef Olakunle Jolaoso,Kazeem Olalekan Aremu 경북대학교 자연과학대학 수학과 2024 Kyungpook mathematical journal Vol.64 No.1
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
Hammed Anuoluwapo Abass,Olawale Kazeem Oyewole 대한수학회 2024 대한수학회논문집 Vol.39 No.2
In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.