New iterative scheme with strict pseudo-contractions and multivalued nonexpansive mappings for fixed point problems and variational inequality problems
Javad Vahidi, Abdul Latif, Mohammad Eslamian · Fixed Point Theory and Applications · 2013
Abstract In this paper, we introduce an iterative scheme for finding a common element of the sets of fixed points for multivalued nonexpansive mappings, strict pseudo-contractive mappings and the set of solutions of an equilibrium problem for a pseudomonotone, Lipschitz-type continuous bifunctions. We prove the strong convergence of the sequence, generated by the proposed scheme, to the solution of the variational inequality. Our results generalize and improve some known results. MSC:47H10, 65K10, 65K15, 90C25.