Strong convergence theorems for families of nonlinear mappings with generalized parameters in Hilbert spaces

Abstract

In this research, motivated and inspired by the above facts, we introduce a new iterative scheme for finding a common element of the set of fixed points of three nonexpansive mappings, and the set of solutions of a mixed equilibrium problem in a real Hilbert space. Strong convergence results are derived under suitable conditions in a real Hilbert space. We introduce a new iterative scheme for finding common solutions of a variational inequality for an inverse-strongly accretive mapping and the solutions of a fixed point problem for a nonexpansive semigroup by using the modified Mann iterative method. We shall prove the strong convergence theorem in a $q$-uniformly smooth Banach spaces under some parameters controlling conditions.