# Strong convergence of viscosity approximation methods with strong pseudocontraction for Lipschitz pseudocontractive mappings

Strong convergence of viscosity approximation methods with strong pseudocontraction for Lipschitz... In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by $$x_{n+1} = (1-\alpha_n-\beta_n)x_n+\alpha_nf(x_n)+\beta_nTx_n$$ , where f is a Lipschitz strong pseudocontractive mapping and {β n }, {α n } satisfy (i) $$\lim\limits_{n\to\infty}\alpha_n = 0$$ ; (ii) $$\sum\limits_{n=1}^\infty \alpha_n = \infty$$ ; (iii) $$\lim\limits_{n\to\infty}\frac{\beta_n^2}{\alpha_n} = 0$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Strong convergence of viscosity approximation methods with strong pseudocontraction for Lipschitz pseudocontractive mappings

, Volume 13 (4) – Nov 24, 2008
13 pages

/lp/springer_journal/strong-convergence-of-viscosity-approximation-methods-with-strong-xF0J3IndMN
Publisher
Birkhäuser-Verlag
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2246-3
Publisher site
See Article on Publisher Site

### Abstract

In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by $$x_{n+1} = (1-\alpha_n-\beta_n)x_n+\alpha_nf(x_n)+\beta_nTx_n$$ , where f is a Lipschitz strong pseudocontractive mapping and {β n }, {α n } satisfy (i) $$\lim\limits_{n\to\infty}\alpha_n = 0$$ ; (ii) $$\sum\limits_{n=1}^\infty \alpha_n = \infty$$ ; (iii) $$\lim\limits_{n\to\infty}\frac{\beta_n^2}{\alpha_n} = 0$$ .

### Journal

PositivitySpringer Journals

Published: Nov 24, 2008

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