Weak convergence theorem by a new extragradient method for fixed point problems and variational inequality problems

English (OpenAlex)

We introduce a new extragradient iterative process, motivated and inspired by [S.H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69],for …nding a common element of the set of …xed points of a nonexpansive mapping and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a Hilbert space.Using this process, we prove a weak convergence theorem for the class of nonexpansive mappings in Hilbert spaces.Finally, as an application, we give some theorems by using resolvent operator and strictly pseudocontractive mapping.