Taiwanese Journal of Mathematics

ISHIKAWA ITERATION WITH ERRORS FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE

L. C. Zeng, G. M. Lee, and N. C. Wong

Full-text: Open access

Abstract

Let $q \gt 1$ and $E$ be a real $q−$uniformly smooth Banach space. Let $K$ be a nonempty closed convex subset of $E$ and $T : K \to K$ be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn [1]. Let $\{u_n\}$ be a bounded sequence in $K$ and $\{\alpha_n\}, \{\beta_n\}, \{\gamma_n\}$ be real sequences in $[0,1]$ satisfying some restrictions. Let $\{x_n\}$ be the bounded sequence in $K$ generated from any given $x_1 \in K$ by the Ishikawa iteration method with errors: $y_n = (1 − \beta_n) x_n + \beta_n Tx_n$, $x_{n+1} = (1 − \alpha_n − \gamma_n) x_n + \alpha_n Ty_n + \gamma_n u_n$, $n \geq 1$. It is shown in this paper that if $T$ is compact or demicompact, then $\{x_n\}$ converges strongly to a fixed point of $T$.

Article information

Source
Taiwanese J. Math., Volume 10, Number 1 (2006), 87-99.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403801

Digital Object Identifier
doi:10.11650/twjm/1500403801

Mathematical Reviews number (MathSciNet)
MR2186164

Zentralblatt MATH identifier
1107.47058

Subjects
Primary: 49H09 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
Ishikawa iteration method with errors strictly pseudocontractive mappings of Browder-Petryshyn type fixed point $q-$Uniformly smooth Banach space

Citation

Zeng, L. C.; Lee, G. M.; Wong, N. C. ISHIKAWA ITERATION WITH ERRORS FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE. Taiwanese J. Math. 10 (2006), no. 1, 87--99. doi:10.11650/twjm/1500403801. https://projecteuclid.org/euclid.twjm/1500403801


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