The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy set by Zadeh, where the concept of uncertainty has been introduced in the theory of sets in a non probabilistic manner. The several researchers were conducting the generalization of the concept of fuzzy sets. The present research paper focuses on the existence of fixed points in fuzzy metric space. Hardy-Rogers is to establish a fixed point theorem for three maps of a complete metric space. The contractive condition is generalized and the commuting condition of Jungck is replaced by the concept of weakly commuting. The three Hardy-Rogers type mappings are extended in fuzzy metric space and also extend to generalize non-expansive mapping define over a compact fuzzy metric space. The contractive condition is generalization of Hardy-Rogers and the commuting condition of Jungck is replace by the concept of weakly commuting. Our results deals with mappings satisfying a condition weaker than commutativity in complete fuzzy metric space and is the generalization in complete fuzzy metric space of Hardy-Rogers type mappings in complete metric space. We also provide some illustrative example to support our result. We apply also our main results to derive unique and common fixed point for contractive mappings.
| Published in | Pure and Applied Mathematics Journal (Volume 8, Issue 6) |
| DOI | 10.11648/j.pamj.20190806.11 |
| Page(s) | 93-99 |
| 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), 2019. Published by Science Publishing Group |
Weakly Commuting Mapping, Asymptotically Regular Mapping, Compact Fuzzy Metric Space, Fixed Point
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APA Style
Mohit Kumar, Ritu Arora, Ajay Kumar. (2019). Hardy-Rogers Type Mappings for Fuzzy Metric Space. Pure and Applied Mathematics Journal, 8(6), 93-99. https://doi.org/10.11648/j.pamj.20190806.11
ACS Style
Mohit Kumar; Ritu Arora; Ajay Kumar. Hardy-Rogers Type Mappings for Fuzzy Metric Space. Pure Appl. Math. J. 2019, 8(6), 93-99. doi: 10.11648/j.pamj.20190806.11
AMA Style
Mohit Kumar, Ritu Arora, Ajay Kumar. Hardy-Rogers Type Mappings for Fuzzy Metric Space. Pure Appl Math J. 2019;8(6):93-99. doi: 10.11648/j.pamj.20190806.11
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Download@article{10.11648/j.pamj.20190806.11,
author = {Mohit Kumar and Ritu Arora and Ajay Kumar},
title = {Hardy-Rogers Type Mappings for Fuzzy Metric Space},
journal = {Pure and Applied Mathematics Journal},
volume = {8},
number = {6},
pages = {93-99},
doi = {10.11648/j.pamj.20190806.11},
url = {https://doi.org/10.11648/j.pamj.20190806.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20190806.11},
abstract = {The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy set by Zadeh, where the concept of uncertainty has been introduced in the theory of sets in a non probabilistic manner. The several researchers were conducting the generalization of the concept of fuzzy sets. The present research paper focuses on the existence of fixed points in fuzzy metric space. Hardy-Rogers is to establish a fixed point theorem for three maps of a complete metric space. The contractive condition is generalized and the commuting condition of Jungck is replaced by the concept of weakly commuting. The three Hardy-Rogers type mappings are extended in fuzzy metric space and also extend to generalize non-expansive mapping define over a compact fuzzy metric space. The contractive condition is generalization of Hardy-Rogers and the commuting condition of Jungck is replace by the concept of weakly commuting. Our results deals with mappings satisfying a condition weaker than commutativity in complete fuzzy metric space and is the generalization in complete fuzzy metric space of Hardy-Rogers type mappings in complete metric space. We also provide some illustrative example to support our result. We apply also our main results to derive unique and common fixed point for contractive mappings.},
year = {2019}
}
TY - JOUR T1 - Hardy-Rogers Type Mappings for Fuzzy Metric Space AU - Mohit Kumar AU - Ritu Arora AU - Ajay Kumar Y1 - 2019/12/24 PY - 2019 N1 - https://doi.org/10.11648/j.pamj.20190806.11 DO - 10.11648/j.pamj.20190806.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 93 EP - 99 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20190806.11 AB - The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy set by Zadeh, where the concept of uncertainty has been introduced in the theory of sets in a non probabilistic manner. The several researchers were conducting the generalization of the concept of fuzzy sets. The present research paper focuses on the existence of fixed points in fuzzy metric space. Hardy-Rogers is to establish a fixed point theorem for three maps of a complete metric space. The contractive condition is generalized and the commuting condition of Jungck is replaced by the concept of weakly commuting. The three Hardy-Rogers type mappings are extended in fuzzy metric space and also extend to generalize non-expansive mapping define over a compact fuzzy metric space. The contractive condition is generalization of Hardy-Rogers and the commuting condition of Jungck is replace by the concept of weakly commuting. Our results deals with mappings satisfying a condition weaker than commutativity in complete fuzzy metric space and is the generalization in complete fuzzy metric space of Hardy-Rogers type mappings in complete metric space. We also provide some illustrative example to support our result. We apply also our main results to derive unique and common fixed point for contractive mappings. VL - 8 IS - 6 ER -
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