An iterative algorithm for fixed point problem and convex minimization problem with applications

In this paper we prove the strong convergence of an iterative sequence for finding a common element of the fixed points set of a strictly pseudocontractive mapping and the solution set of the constrained convex minimization problem for a convex and continuously Fréchet differentiable functional in a real Hilbert space. We apply our result to solving the split feasibility problem and the convexly constrained linear inverse problem involving the fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space.