Geodesic
Hybrid inertial accelerated extragradient algorithms for split pseudomonotone equilibrium problems and fixed point problems of demicontractive mappings
Filomat, Tome 37 (2023) no. 5, p. 1607

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DOI

In this paper, we present a new hybrid extragradient algorithm for finding a common element of the fixed point problem for a demicontractive mapping and the split equilibrium problem for a pseu-domonotone and Lipschitz-type continuous bifunction. By using a new technique of choosing the step size of the proposed method, our algorithms do not need any prior information of the operator norm. In fact, we propose an inertial type algorithm in order to accelerate its convergence rate and then prove strong convergence theorem of our proposed method under some control conditions. Moreover, we give some numerical experiments to support our main results.
DOI : 10.2298/FIL2305607H
Classification : 47H09, 47H05, 68W25
Keywords: extragradient algorithm, fixed point problem, split equilibrium problem, Hilbert space 
Adisak Hanjing; Suthep Suantai; Yeol Je Cho. Hybrid inertial accelerated extragradient algorithms for split pseudomonotone equilibrium problems and fixed point problems of demicontractive mappings. Filomat, Tome 37 (2023) no. 5, p. 1607 . doi: 10.2298/FIL2305607H
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     author = {Adisak Hanjing and Suthep Suantai and Yeol Je Cho},
     title = {Hybrid inertial accelerated extragradient algorithms for split pseudomonotone equilibrium problems and fixed point problems of demicontractive mappings},
     journal = {Filomat},
     pages = {1607 },
     year = {2023},
     volume = {37},
     number = {5},
     doi = {10.2298/FIL2305607H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305607H/}
}
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