A note on the rate of convergence of viscosity iterations

In [6], Moudafi introduced the so-called viscosity iter- ative method to approximate a fixed point of a nonexpansive map- ping and proved the strong convergence of the generated sequence. Since then, several authors extended the convergence result in dif- ferent settings and for mappings satisfying general metric condi- tions. Anyway, to the best of our knowledge and beside numerical simulations, little is known about the speed of convergence of the method itself. In this paper, we propose a step in this direction by giving an estimate for the rate of convergence of viscosity se- quences generated by quasi-nonexpansive mappings in the setting of q-uniformly smooth Banach spaces.