Convergence theorems by hybrid projection methods for Lipschitz-continuous monotone mappings and a countable family of nonexpansive mappings

• Autorzy: Somyot Plubtieng , Poom Kumam
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce two iterative schemes for finding a common element of the set of a common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a Hilbert space by using the hybrid projection methods in the mathematical programming. Then we prove strong convergence theorems by the hybrid projection methods for a monotone, Lipschitz-continuous mapping and a countable family of nonexpansive mappings. Moreover, we apply our result to the problem for finding a common fixed point of two mappings, such that one of these mappings is nonexpansive and the other is taken from the more general class of Lipschitz pseudocontractive mappings. Our results extend and improve the results of Nadezhkina and Takahashi [SIAM J. Optim. 16 (2006), 1230-1241], Zeng and Yao [Taiwanese J. Math. 10 (2006), 1293-1303] and many authors.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47D03: Groups and semigroups of linear operators
• 47H10: Fixed-point theorems
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 283-297

Daty

wydano

2011

Twórcy

autor

Somyot Plubtieng

• Department of Mathematics, Faculty of Science, Naresuan University, Pitsanulok 65000, Thailand

autor

Poom Kumam

• Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

Identyfikatory

DOI

10.4064/bc92-0-20