A hybrid extragradient method for solving pseudomonotone equilibrium problems using Bregman distance

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

“…Some numerical examples are presented to show the efficiency and accuracy of the proposed method. This result improves and extends the results of [17][18][19][20]22,25,47,[49][50][51] and many other results in the literature.…”

“…(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.…”

“…It is worth noting that the results of Anh, Hieu and Eskandani et al, mentioned above, and other similar ones (see, e.g., [20][21][22]) involve prior knowledge of the Lipschitz-like constants, which have been proven to be very strenuous to approximate piratically. In fact, when it is possible, the estimates are often too small, which slows down the rate of convergence of the algorithms.…”

A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

“…Then the function f is said to be uniformly smooth on bounded subsets if lim We recall from [27] that the normal cone N C to C at a point x ∈ C is defined by…”

Approximation solutions of quasi-equilibrium problems in Banach spaces

“…Recently many researchers have studied approximation of solutions of an equilibrium problem (see, e.g. [6], [9], [10], [15], [16], [18] and references therein). Equilibrium problems with monotone and pseudo-monotone bifunctions have been studied extensively in Hilbert, Banach as well as in topological vector spaces by many c 2020 Miskolc University Press authors (e.g.…”