Strong convergence of shrinking projection methods for a family of pseudocontractive mappings in Hilbert spaces

The shrinking projection method has gained more and more attention as a powerful tool for the approximation of a fixed point of nonlinear mappings. In this paper, we introduce a new shrinking projection method for the approximation of fixed points of a family of pseudocontractive mappings in a Hilbert space. Using this method, we also deal with the problem of finding a common zero of a family of monotone operators and obtain a strong convergence theorem.