Abstract
In the present paper, we propose three kinds of new algorithms for a finite family of quasi-asymptotically pseudocontractive mappings in real Hilbert spaces. By using some new analysis techniques, we prove the strong convergence of the proposed algorithms. Some numerical examples are also included to illustrate the effectiveness of the proposed algorithms. The results presented in this paper are interesting extensions of those well-known results.
Highlights
Throughout this paper, we assume that H is a real Hilbert space with inner product ·, · and the induced norm ·, respectively
The purpose of this paper is to propose three kinds of new hybrid projection algorithms for constructing a common fixed point of a finite family of quasi-asymptotically pseudocontractive mappings in a real Hilbert space
3 Main results we present three kinds of new hybrid projection algorithms for finding a common fixed point for a finite family of uniformly Li-Lipschitzian and quasiasymptotically pseudocontractive mappings in Hilbert spaces
Summary
Throughout this paper, we assume that H is a real Hilbert space with inner product ·, · and the induced norm · , respectively. The purpose of this paper is to propose three kinds of new hybrid projection algorithms for constructing a common fixed point of a finite family of quasi-asymptotically pseudocontractive mappings in a real Hilbert space. Theorem Z Let C be a nonempty, bounded, and closed convex subset of a real Hilbert space H and T : C → C be a uniformly L-Lipschitzian and asymptotically pseudocontractive mapping which is uniformly asymptotically regular, i.e., limn→∞ supx∈C{ Tn+ x – Tnx } =. We prove the following strong convergence theorem for a finite family of uniformly Li-Lipschitzian and quasi-asymptotically pseudocontractive mappings in Hilbert spaces. We consider a simpler algorithm for a finite family of uniformly Li-Lipschitzian and quasi-asymptotically pseudocontractive mappings in real Hilbert spaces. The work related to other iterative methods for asymptotically pseudocontractive mappings can be found in [ – ]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
