Strong convergence by a hybrid algorithm for solving generalized mixed equilibrium problems and fixed point problems of a Lipschitz pseudo-contraction in Hilbert spaces

摘要

In this paper, we construct a sequence by using some appropriated closed convex sets based on the hybrid shrinking projection methods to find a common solution of fixed point problems of a Lipschitz pseudo-contraction and generalized mixed equilibrium problems in Hilbert spaces. The strong convergence theorems are proved under some mild conditions on scalars. The results not only cover the research work of Yao et al. (Nonlinear Anal. 71:4997-5002, 2009) but can also be applied for finding the common element of the set of zeroes of a Lipschitz monotone mapping and the set of generalized mixed equilibrium problems in Hilbert spaces. MSC:47H05, 47H09, 47H10, 47J25.