A General Iterative Method Based on the Hybrid Steepest Descent Scheme for Nonexpansive Mappings in Hilbert Spaces

@article{Tian2010AGI,
title={A General Iterative Method Based on the Hybrid Steepest Descent Scheme for Nonexpansive Mappings in Hilbert Spaces},
author={Ming Tian},
journal={2010 International Conference on Computational Intelligence and Software Engineering},
year={2010},
pages={1-4}
}

Let $H$ be a real Hilbert space.Suppose that $T$ is a nonexpansive mapping on $H$ with a fixed point ,$G$ is a $L-$Lipschitzian mapping on $H$ with coefficient $L>0$,and $F:H\rightarrow H$ is a $k-$ Lipschitzian and $\eta-$strongly monotone operator with $k>0,\eta>0$.Let $0<\mu<2\eta/k^{2},0<\gamma<\mu(\eta-\frac{\mu k^{2}}{2})/L=\tau/L$. We pointed out the relationship between Yamada's method and viscosity iteration and proved that the sequence $\{x_{n}\}$ generated by the iterative method $x_â€¦Â CONTINUE READING