A new strongly convergent algorithm to solve pseudo-monotone equilibrium problems in a real Hilbert space
Kanikar Muangchoo · Journal of Mathematics and Computer Science · 2021
The purpose of this research is to formulate a new algorithm by combining a viscosity-type method with the extragradient algorithm and explicit step size rule to figure out the equilibrium problems involving pseudo-monotone and Lipschitz-type continuous bi-function in a real Hilbert space. A strong convergence theorem is well-established by the use of certain mild conditions on the bi-function, as well as some conditions on the iterative control parameters. The designed algorithm uses a non-monotonic step size rule based on the local bi-function information. Applications of the main results are also presented to solve variational inequalities and fixed-point problems. The computational behaviour of the designed algorithm on a test problem is performed related to other existing algorithms.