Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces
In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete <i>b</i>-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a c...
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doaj-dce6842b6454418c9762cdab2b7bf6eb2020-11-24T22:02:54ZengMDPI AGSymmetry2073-89942018-10-01101155510.3390/sym10110555sym10110555Some Globally Stable Fixed Points in <i>b</i>-Metric SpacesUmar Yusuf Batsari0Poom Kumam1Kanokwan Sitthithakerngkiet2KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandKMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, ThailandIn this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete <i>b</i>-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the <i>b</i>-metric function has the regularity property. Our results improve, and generalize some current results in the literature.https://www.mdpi.com/2073-8994/10/11/555fixed pointglobally stable fixed pointasymptotically contractive mappingregularity conditionorder preserving mappingaltering distance function |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Umar Yusuf Batsari Poom Kumam Kanokwan Sitthithakerngkiet |
spellingShingle |
Umar Yusuf Batsari Poom Kumam Kanokwan Sitthithakerngkiet Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces Symmetry fixed point globally stable fixed point asymptotically contractive mapping regularity condition order preserving mapping altering distance function |
author_facet |
Umar Yusuf Batsari Poom Kumam Kanokwan Sitthithakerngkiet |
author_sort |
Umar Yusuf Batsari |
title |
Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces |
title_short |
Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces |
title_full |
Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces |
title_fullStr |
Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces |
title_full_unstemmed |
Some Globally Stable Fixed Points in <i>b</i>-Metric Spaces |
title_sort |
some globally stable fixed points in <i>b</i>-metric spaces |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2018-10-01 |
description |
In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete <i>b</i>-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the <i>b</i>-metric function has the regularity property. Our results improve, and generalize some current results in the literature. |
topic |
fixed point globally stable fixed point asymptotically contractive mapping regularity condition order preserving mapping altering distance function |
url |
https://www.mdpi.com/2073-8994/10/11/555 |
work_keys_str_mv |
AT umaryusufbatsari somegloballystablefixedpointsinibimetricspaces AT poomkumam somegloballystablefixedpointsinibimetricspaces AT kanokwansitthithakerngkiet somegloballystablefixedpointsinibimetricspaces |
_version_ |
1725834038103506944 |