Modified Popov's Subgradient Extragradient Algorithm With Inertial Technique for Equilibrium Problems and Its Applications

A Parallel Hybrid Bregman Subgradient Extragradient Method for a System of Pseudomonotone Equilibrium and Fixed Point Problems

“…Then, the sequences {x n }, {y i n }, {z i n } generated by Algorithm 2 converges strongly to a solution x * , where x * = Proj f Sol (x 0 ). Furthermore, by setting N = M = 1, we obtain the following result, which extends the results of [24,25,51] to a real reflexive Banach space.…”

“…(iii) Furthermore, when E is the real Hilbert space, our Algorithm 1 improves the algorithms of [18,[47][48][49][50] in the setting of real Hilbert spaces. (iv) Furthermore, when E is a real Hilbert space and N = 1, M = 1, our Algorithm 1 improves and compliments the algorithms of [17,20,22,24,25,51]. Now, to prove the strong convergence of the algorithm parallel hybrid Bregman subgradient extragradient method (PHBSEM), we need the following results.…”

“…Thus, it becomes very important to find an algorithm that does not depend on the prior knowledge of the Lipschitz-like constants. Recently, the authors of [23][24][25], introduced some modified extragradient algorithms for solving the pseudomonotone EP (when N = 1), which does not involve the prior estimate of the Lipschitz-like constants c 1 and c 2 . Furthermore, related to our work are several methods such as [26], where the stepsize is the variable stepsize formula, that is the bifunction has a Lipschitz-like condition defined on it, and the algorithm also operates without the prior estimation of Lipschitz-type constants.…”

“…Recently, the authors of [23][24][25], introduced some modified extragradient algorithms for solving the pseudomonotone EP (when N = 1), which does not involve the prior estimate of the Lipschitz-like constants c 1 and c 2 . Furthermore, related to our work are several methods such as [26], where the stepsize is the variable stepsize formula, that is the bifunction has a Lipschitz-like condition defined on it, and the algorithm also operates without the prior estimation of Lipschitz-type constants. The authors in [27,28] considered algorithms for solving the mixed equilibrium problem, split variational inclusion and fixed point theorems.…”