General iterative algorithm for demicontractive-type mapping in real Hilbert spaces

In this paper, we investigate the problem of finding a solution  to fixed point problem involving demicontractive mappings in the framework of Hilbert spaces. Inspired by general iterative algorithm, a new iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established without any compactness assumption. Our theorems are significant improvements on several important recent results.