Some Results in Hausdorff Neutrosophic Metric Spaces on Hutchinson-Barnsley Operator
DOI:
https://doi.org/10.23755/rm.v43i0.782Keywords:
Contraction, Hutchinson-Barnsley Operator, Metric Space, Hausdorff Neutrosophic Metric Spaces, HyperspaceAbstract
The main purpose of this paper is to prove the Neutrosophic contraction properties of the Hutchinson-Barnsley operator on the Neutrosophic hyperspace with respect to the Hausdorff Neutrosophic metrics. Also we discuss about the relationships between the Hausdorff Neutrosophic metrics on the Neutrosophic hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the Neutrosophic metric spaces.References
B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 1983.
J. E. Hutchinson, Fractals and self similarity, Indiana University Mathematics Journal, 30 (1981) 713-747.
M. Barnsley, Fractals Everywhere, 2nd ed., Academic Press, USA, 1993.
M. Barnsley, Super Fractals, Cambridge University Press, New York,2006.
D. Easwaramoorthy and R. Uthayakumar, Analysis on Fractals in Fuzzy Metric Spaces, Fractals, 19(3) (2011) 379-386.
R. Uthayakumar and D. Easwarmoorthy, Hutchinson-Barnsley Operator in Fuzzy Metric Spaces, International Journal of Engineering and Natural Sciences, 5(4) (2011) 203-207.
K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, (1986), 87-96.
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004) 1039-1046.
Smarandache, F. (2005) Neutrosophic set, a generalization of the intuitionistic Fuzzy sets and Systems,20, 191-210.
Smarandache, F. (2003) A unifying field in logics: Neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics. Phoenix, Xiquan, (2003)
Abdel-Basset, M., et al. An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing 77: 438-452, (2019).
Murat Kirisci and Necip Simsek, Neutrosopohic Metric Spaces, Mathematical Sciences, Islamic Azad University, 2020.
Jeyaraman at el, Fixed point results in non-Archimedean generalized intuitionistic fuzzy metric spaces, Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), pages 48-58.
Jeyaraman at el, Some new fixed point theorems in generalized intuitionistic fuzzy metric spaces, Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 3, pages 42-52.
Sowndrarajan, Jeyaraman and Florentin Smarandache, Fixed point results for contraction theorems in neutrosophic metric spaces, Neutrosophic Sets and Systems, Vol. 36 2020, University of New Mexico.
Downloads
Published
Issue
Section
License
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:
- Free access for all users worldwide
- Increased visibility and readership
- Rapid publication
- No spatial constraints
- Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)
Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.