A new approach to solving strongly pseudomonotone equilibrium problems in Banach spaces using Bregman distance
Subject Areas : Mathematical AnalysisRoushanak Lotfikar 1 , Gholam reza Zamani Eskandani 2
1 - Faculty of Basic Science, Ilam University, Ilam, Iran.
2 - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Keywords: Extragradient method, Strongly Pseudomonotone bifunction, Legendre function, Bregman Lipschitz-type condition,
Abstract :
In this article, we introduce new algorithms for solving equilibrium problem involving strongly pseudomonotone and Bregman Lipschitz-type bifunction in reflexive Banach spaces. The algorithm is constructed around the extragradient method and the advantage of the algorithm is that it is done without the prior knowledge of Bregman Lipschitz coefficients. Theorem of strong convergence is established under mild conditions.
