Strong Convergence for a Strongly Quasi-Nonexpansive Sequence in Hilbert Spaces

We prove a strong convergence theorem for strongly quasi-nonexpansive sequence of mappings in Hilbert spaces. Moreover, we can improve the recent results of Tian and Jin (2011). We also give a simple proof of Marino-Xu’s result (2006)

On the Strong Convergence of Viscosity Approximation Process for Quasinonexpansive Mappings in Hilbert Spaces

We improve the viscosity approximation process for approximation of a fixed point of a quasi-nonexpansive mapping in a Hilbert space proposed by Maingé (2010). An example beyond the scope of the previously known result is given