Paper Info
Title
Some observations on generalized non-expansive mappings with an application
Abstract
This study aimed at showing that the classes of generalized non-expansive mappings due to Hardy and Rogers and the mappings satisfying Suzuki’s condition (C) are independent and study some basic properties of generalized non-expansive mappings. Also, we introduce a new iterative scheme, called JF iterative scheme, and prove convergence results for generalized non-expansive mappings due to Hardy and Rogers in uniformly convex Banach spaces. Moreover, we show numerically that JF iterative scheme converges to a fixed point of generalized non-expansive mappings faster than some known and leading iterative schemes. As an application, we utilize newly defined iterative scheme to approximate the solution of a delay differential equation. Also, we present some nontrivial illustrative numerical examples to support main results. Our results are new and extend several relevant results in the existing literature.
Year
DOI
Venue
2020
10.1007/s40314-020-1101-4
Computational and Applied Mathematics
Keywords
DocType
Volume
Generalized non-expansive mappings, Suzuki’s condition (C), Fixed points, JF iterative scheme, uniformly convex Banach spaces, 47H09, 47H10
Journal
39
Issue
ISSN
Citations 
2
2238-3603
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Faeem Ali100.34
Javid Ali242.69
Juan J. Nieto355981.45