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.

A note on the rate of convergence of viscosity iterations

Vittorio Colao
In corso di stampa

Abstract

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.
Nonexpansive mapping, contractive mapping, iterative method, uniform smooth Banach space, duality map
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/308612
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