Abstract
AbstractWe introduce a new iterative scheme for finding the common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings, and the problem of finding a zero of a monotone operator. This main theorem extends a recent result of Yao et al. (2007) and many others.
Highlights
Let H be a real Hilbert space with inner product ·, · and norm ·, and let C be a closed convex subset of H
Let F be a bifunction of C × C into R, where R is the set of real numbers
In 1997, Flam and Antipin 1 introduced an iterative scheme of finding the best approximation to initial data when EP φ is nonempty and proved a strong convergence theorem
Summary
Let H be a real Hilbert space with inner product ·, · and norm · , and let C be a closed convex subset of H. Aoyama et al 12 introduced an iterative scheme for finding a common fixed point of a countable family of nonexpansive mappings in Banach spaces and obtained the strong convergence theorem for such scheme. Takahashi and Aoyama et al , we introduce a new extragradient method 4.2 which is mixed the iterative schemes considered in 10–12 for finding a common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the solution set of the classical variational inequality problem for a monotone L-Lipschitz continuous mapping in a real Hilbert space. The results obtained in this paper improve and extend the recent ones announced by Yao et al results 10 and many others
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
