ON STRONG CONVERGENCE OF HALPERN’S METHOD FOR QUASI-NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Jesús Garcı́a Falset, Enrique Llorens-Fuster, Giuseppe Marino, Angela Rugiano · Mathematical Modelling and Analysis · 2016
In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.