Taiwanese Journal of Mathematics

GENERALIZED PROJECTION AND ITERATIVE METHODS FOR APPROXIMATING FIXED POINTS OF ASYMPTOTICALLY WEAKLY SUPPRESSIVE OPERATORS

L. C. Ceng, S. Huang, and A. Petrusel

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Abstract

Let $C$ be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space $E$, let $S: C \to C$ be a relatively nonexpansive mapping, and let $T: C \to E$ be an asymptotically weakly suppressive operator. Using the notion of generalized projection, iterative methods for approximating common fixed points of the mappings $S$ and $T$ are studied. In terms of the modified Ishikawa iteration and modified Halpern one for relatively nonexpansive mappings, we propose two modified versions of Chidume, Khumalo and Zegeye's iterative algorithms [C.E. Chidume, M. Khumalo and H. Zegeye, Generalized projection and approximation of fixed points of nonself maps, J. Appro. Theory, 120 (2003) 242-252] for finding approximate common fixed points of the mappings $S$ and $T$. Moreover, it is proved that these two iterative algorithms converge strongly to the same common fixed point of the mappings $S$ and $T$.

Article information

Source
Taiwanese J. Math., Volume 14, Number 1 (2010), 59-80.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405728

Digital Object Identifier
doi:10.11650/twjm/1500405728

Mathematical Reviews number (MathSciNet)
MR2603443

Zentralblatt MATH identifier
1192.47053

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
relatively nonexpansive mapping asymptotically weakly suppressive operator generalized projection iterative methods uniformly convex and uniformly smooth Banach space strong convergence

Citation

Ceng, L. C.; Huang, S.; Petrusel, A. GENERALIZED PROJECTION AND ITERATIVE METHODS FOR APPROXIMATING FIXED POINTS OF ASYMPTOTICALLY WEAKLY SUPPRESSIVE OPERATORS. Taiwanese J. Math. 14 (2010), no. 1, 59--80. doi:10.11650/twjm/1500405728. https://projecteuclid.org/euclid.twjm/1500405728


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