A new contribution to discontinuity at fixed point
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909639670497280 |
|---|---|
| author | Taş, Nihal Özgür, Nihal Yilmaz |
| author_facet | Taş, Nihal Özgür, Nihal Yilmaz |
| contents | The aim of this paper is to obtain new solutions to the open question on the existence of a contractive condition which is strong enough to generate a fixed point but which does not force the map to be continuous at the fixed point. To do this, we use the right-hand side of the classical Rhoades' inequality and the number $M(x,y)$ given in the definition of an $(α,β)$-Geraghty type-$I$ rational contractive mapping. Also we give an application of these new results to discontinuous activation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_03699 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A new contribution to discontinuity at fixed point Taş, Nihal Özgür, Nihal Yilmaz Metric Geometry Primary 47H10, Secondary 54H25, 47H09 The aim of this paper is to obtain new solutions to the open question on the existence of a contractive condition which is strong enough to generate a fixed point but which does not force the map to be continuous at the fixed point. To do this, we use the right-hand side of the classical Rhoades' inequality and the number $M(x,y)$ given in the definition of an $(α,β)$-Geraghty type-$I$ rational contractive mapping. Also we give an application of these new results to discontinuous activation functions. |
| title | A new contribution to discontinuity at fixed point |
| topic | Metric Geometry Primary 47H10, Secondary 54H25, 47H09 |
| url | https://arxiv.org/abs/1705.03699 |