Research Article
On Firmly Non-Expansive Mappings
- Akenten Appiah-Menka University of skills Training and Entrepreneurial Development
* Corresponding author
Abstract
In this paper, it is shown that for a closed convex subset C and to every non-expansive mapping T:C->C, one can associate a firmly non-expansive mapping with the same fixed point set as T in a given Banach space.
How to Cite
J. F. Gordon, E. O. Gyasi, On Firmly Non-Expansive Mappings, Int. J. Anal. Appl. 19 (2021), 512–517. https://doi.org/10.28924/2291-8639-19-2021-512
BibTeX
@article{Gordon2021,
author = {Gordon, Joseph Frank and Gyasi, Esther Opoku},
title = {On Firmly Non-Expansive Mappings},
journal = {Int. J. Anal. Appl.},
volume = {19},
year = {2021},
pages = {512--517},
doi = {10.28924/2291-8639-19-2021-512}
}References
- [1] F.E. Browder, Nonlinear monotone operators and convex sets in banach spaces. Bull. Amer. Math. Soc. 71(5) (1965), 780-785.
- [2] F.E. Browder, Nonexpansive nonlinear operators in a Banach space. Proc. Nat. Acad. Sci. USA, 54(4) (1965), 1041-1044.
- [3] F.E. Browder, Convergence theorems for sequences of nonlinear operators in banach spaces. Math. Zeitschr. 100(3) (1976), 201-225.
- [4] F.E. Browder, W.V. Petryshyn. The solution by iteration of nonlinear functional equations in banach spaces. Bull. Amer. Math. Soc. 72(3) (1966), 571-575.
- [5] F.E. Browder, W.V. Petryshyn. Construction of fixed points of nonlinear mappings in Hilbert space. J. Math. Anal. Appl. 20(2) (1967), 197-228.
- [6] W. Kirk. A fixed point theorem for mappings which do not increase distances. Amer. Math. Mon. 72(9) (1965), 1004-1006.
- [7] J. George, Minty et al. Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29(3) (1962), 341-346.
- [8] R. Bruck. Nonexpansive projections on subsets of Banach spaces. Pac. J. Math. 47(2) (1973), 341-355.
- [9] R. Smarzewski. On firmly nonexpansive mappings. Proc. Amer. Math. Soc. 113(3) (1991), 723-725.
- [10] S. Banach, H. Steinhaus. Sur le principe de la condensation de singularites. Fundam. Math. 1(9) (1927), 50-61.