Proximal forward-backward splitting method for zeros of sum accretive operators for a fixed point set and inverse problems


K. Sitthithakerngkiet - Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut K. Promluang - KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut P. Thounthong - Renewable Energy Research Centre \(\&\) Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut P. Kumam - KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut


In this paper, we investigate regularization method via a proximal point algorithm for solving treating sum of two accretive operators and fixed point problems. Strong convergence theorems are established in the framework of Banach spaces. Also we apply our result to variational inequalities and equilibrium problems. Furthermore, an illustrative numerical example is presented.