Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal monotone operators
The authors consider the problem of finding common solution points of an equilibrium problem with a monotone bi-function and a multi-valued inclusion with monotone mapping in a Banach space. Thus, it is an extension of the problem from the paper by \textit{W. Takahashi} and \textit{K. Zembayashi} [Nonlinear Anal., Theory Methods Appl. 70, No. 1 (A), 45--57 (2009; Zbl 1170.47049)] where a fixed point problem of a non-expansive mapping was used instead of the multi-valued inclusion. In the latter paper, two hybrid proximal point type methods were proposed and their strong and weak convergence was established. The authors adjust those methods to the problem under solution and also prove their strong and weak convergence.
scientific article; zbMATH DE number 5625128
scientific article