Volume 4, Issue 3, September 2018, Pages: 39-43
Received: Aug. 23, 2018;
Accepted: Sep. 19, 2018;
Published: Oct. 12, 2018
Views 615 Downloads 72
Güzide Şenel, Department of Mathematics, Amasya University, Amasya, Turkey
This study is intended as an attempt to bring together the areas of spheres, soft real numbers and soft points. Relating spheres to soft real numbers and soft points provides a natural and intrinsic construction of soft spheres. In this paper a new construction of spheres is provided via soft real numbers and soft points. This new construction sheds light on soft sphere applications for analyzing the locus of them. Also, several related results have been obtained. It is proved that spheres play an important role in the theory of soft metric spaces with taking into consideration soft points. This viewpoint sheds some new light on soft sphere examples and drawings for analyzing the locus of them. This new approach may be the starting point for soft mathematical concepts and structures based on soft set-theoric operations in soft metric spaces and stimulate the reader to further research.
A New Construction of Spheres Via Soft Real Numbers and Soft Points, Mathematics Letters.
Vol. 4, No. 3,
2018, pp. 39-43.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
D. Molodtsov, Soft set theory-first results, Comput. Math. Appl.(37) (1999) 19-31.
M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553.
N. Cagman and S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl.(59)(2010), 3308-3314.
S. Das and S.K. Samanta, Soft Metric Spaces, Annals of Fuzzy Mathematics and Informatics, 6(1) (2013) 77-94.
G. Senel, The Parameterization Reduction of Soft Point and its Applications with Soft Matrix, International Journal of Computer Applications, (164) (1) (2017), 1-6.
S. Das and S.K. Samanta, Soft Real Sets, Soft Real Numbers and Their Properties, J. Fuzzy Math. 20 (3) (2012) 551-576.
S. Das and S.K. Samanta, On soft complex sets and soft complex numbers, The Journal of Fuzzy Mathematics (21)(1) (2013) 195-216.
A. Dress, K. T. Huber, V. Moulton, Metric Spaces in Pure and Applied Mathematics, Documenta Mathematica Quadratic Forms LSU (2001), 121-139.
S. Semmes, Some Remarks About Metric Spaces, Spherical Mappings, Functions and Their Derivatives, Publicacions Matem‘atiques 40(1996), 411-430.
A. Aygunoğlu, H. Aygun, Some notes on soft topological spaces, Neural Comp. Appl. (2011), 521-011-0722-3.
G. Senel, Soft Metric Spaces, Gaziosmanpasa University Graduate School of Natural and Applied Sciences Department of Mathematics Ph.D. Thesis, (2013), 92.