Affiliation:
1. University of Botswana , Department of Mathematics , Gaborone , Botswana
Abstract
Abstract
In this paper, we introduce new iterative methods for approximating common fixed points of two non-self mappings in the framework of real Hilbert spaces. We establish weak and strong convergence results for approximating common fixed points of two nonexpansive non-self mappings. In addition, we establish strong convergence results for approximating common fixed points of two quasi-nonexpansive non-self mappings under appropriate conditions. Our results improve and generalize many of the results in the literature. Moreover, our findings will open the way forward for the study of iterative methods for finding common fixed points of two non-self mappings in Banach spaces more general than Hilbert spaces.
Subject
Applied Mathematics,Geometry and Topology,Algebra and Number Theory
Reference33 articles.
1. [1] N. Shahzad and H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. Theory Methods Appl., 71 (2009), no. 3, 838–844.
2. [2] H. H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert spaces, J. Math Anal. Appl., 202 (1996), 150–159.
3. [3] C.E. Chidume and C.O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl., 318 (2006), no. 1, 288–295.
4. [4] O. A. Daman and H. Zegeye, Strong convergence theorems for a common fixed point of a finite family of pseudocontractive mappings, Int. J. Math. Math. Sci., 2012 (2012), Article ID 405315, 18 pages.
5. [5] G. Das and J. P. Debata, Fixed points of quasinonexpansive mappings, Indian J. Pure Appl. Math., 17 (1986), no. 11, 1263–1269.