On fixed points of fundamentally nonexpansive mappings in Banach spaces
author
Abstract:
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.
similar resources
on fixed points of fundamentally nonexpansive mappings in banach spaces
we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
full textFixed points of multivalued nonexpansive mappings in Banach spaces
* Correspondence: [email protected] Department of Mathematics, Ataturk University, Erzurum 25240, Turkey Full list of author information is available at the end of the article Abstract In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a “strong condition” on the mapping involved in the ite...
full textApproximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...
full textApproximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces
An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space is recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishihawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also exten...
full textApproximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT() spaces
An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space has been recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishikawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also...
full textA new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces
In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.
full textMy Resources
Journal title
volume 7 issue 1
pages 219- 224
publication date 2016-03-05
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023