Geodesic
A New Inertial-Projection Method for Solving Split Generalized Mixed Equilibrium and Hierarchical Fixed Point Problems
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 2, p. 199 .

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In this paper, we introduce a new iterative algorithm of inertial form for approximating the common solution of Split Generalized Mixed Equilibrium Problem (SGMEP) and Hierarchical Fixed Point Problem (HFPP) in real Hilbert spaces. Motivated by the subgradient extragradient method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity and lower semicontinuity of the SGMEP and HFPP associated mappings, we establish the strong convergence of the iterative algorithm. Some numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature.
Classification : 47H09, 49J35, 90C47
Keywords: pseudomonotone, equilibrium problem, hierachical fixed point, inertial, strong convergence, Hilbert space 
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     author = {Olawale Kazeem Oyewole and Oluwatosin Temitope Mewomo},
     title = {A {New} {Inertial-Projection} {Method} for {Solving} {Split} {Generalized} {Mixed} {Equilibrium} and {Hierarchical} {Fixed} {Point} {Problems}},
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Olawale Kazeem Oyewole; Oluwatosin Temitope Mewomo. A New Inertial-Projection Method for Solving Split Generalized Mixed Equilibrium and Hierarchical Fixed Point Problems. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 2, p. 199 . http://geodesic.mathdoc.fr/item/KJM_2024_48_2_a2/