Karahan, İbrahimOzdemir, Murat2026-03-262026-03-2620141303-599110.1501/Commua1_0000000704https://doi.org/10.1501/Commua1_0000000704https://hdl.handle.net/20.500.14901/2205We 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 finding a common element of the set of fixed 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.eninfo:eu-repo/semantics/openAccessVariational InequalitiesFixed Point ProblemsWeak ConvergenceArticle