In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9].
| Published in | Pure and Applied Mathematics Journal (Volume 4, Issue 4) |
| DOI | 10.11648/j.pamj.20150404.14 |
| Page(s) | 159-163 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Fuzzy Metric Spaces, Generalized Contraction Mapping, G-Complete
| [1] | L. B. Ciric. Generalized contractions and fixed-point theorems. Publ. Inst. Math. (Beograd) (N.S.),12(26):19-26, 1971. |
| [2] | L. B. Ciric. Fixed points for generalized multi-valued contractions. Mat. Vesnik, 9(24):265-272,1972. |
| [3] | L. B.Ciric. On fixed points of generalized contractions on probabilistic metric spaces. Publ. Inst.Math. (Beograd) (N.S.), 18(32):71-78, 1975. |
| [4] | A. George and P. Veeramani. On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3):395{399, 1994. |
| [5] | M. Grabiec. Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27(3):385{389, 1988. |
| [6] | V. Gregori and A. Sapena. On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 125(2):245-252, 2002. |
| [7] | I. Kramosil and J. Michalek. Fuzzy metrics and statistical metric spaces. Kybernetika (Prague), 11(5):336-344, 1975. |
| [8] | D.Mihet. Fuzzy-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems, 159(6):739-744, 2008. |
| [9] | E. Pap, O. Hadzic, and R. Mesiar. A fixed point theorem in probabilistic metric spaces and an application. J. Math. Anal. Appl., 202(2):433-449, 1996. |
| [10] | J. u. Rodriguez Lopez and S. Romaguera. The Hausdorff fuzzy metric on compact sets. Fuzzy Sets and Systems, 147(2):273-283, 2004. |
| [11] | S. Romaguera, A. Sapena, and P. Tirado. The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words. Topology Appl., 154(10):2196-2203, 2007. |
| [12] | B. Schweizer and A. Sklar. Statistical metric spaces. Pacic J. Math., 10:313-334, 1960. |
| [13] | R. M. Tardi. Contraction maps on probabilistic metric spaces. J. Math. Anal. Appl., 165(2):517-523, 1992. |
APA Style
Naser Abbasi, Hamid Mottaghi Golshan, Mahmood Shakori. (2015). Fixed-point Theorems in G-complete Fuzzy Metric Spaces. Pure and Applied Mathematics Journal, 4(4), 159-163. https://doi.org/10.11648/j.pamj.20150404.14
ACS Style
Naser Abbasi; Hamid Mottaghi Golshan; Mahmood Shakori. Fixed-point Theorems in G-complete Fuzzy Metric Spaces. Pure Appl. Math. J. 2015, 4(4), 159-163. doi: 10.11648/j.pamj.20150404.14
AMA Style
Naser Abbasi, Hamid Mottaghi Golshan, Mahmood Shakori. Fixed-point Theorems in G-complete Fuzzy Metric Spaces. Pure Appl Math J. 2015;4(4):159-163. doi: 10.11648/j.pamj.20150404.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.20150404.14,
author = {Naser Abbasi and Hamid Mottaghi Golshan and Mahmood Shakori},
title = {Fixed-point Theorems in G-complete Fuzzy Metric Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4},
pages = {159-163},
doi = {10.11648/j.pamj.20150404.14},
url = {https://doi.org/10.11648/j.pamj.20150404.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150404.14},
abstract = {In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9].},
year = {2015}
}
TY - JOUR T1 - Fixed-point Theorems in G-complete Fuzzy Metric Spaces AU - Naser Abbasi AU - Hamid Mottaghi Golshan AU - Mahmood Shakori Y1 - 2015/07/30 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.20150404.14 DO - 10.11648/j.pamj.20150404.14 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 159 EP - 163 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20150404.14 AB - In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9]. VL - 4 IS - 4 ER -
Information
Email: