FUZZY CONE B-METRIC SPACES

Year 2019, Volume: 37 Issue: 4, 1301 - 1314, 01.12.2019

Hande Poşul Elif Kaplan Servet Kütükcü

Abstract

In this article, we present the theory of fuzzy cone b-metric space as a new type of generalized metric spaces. We give some basic properties of this new space as Hausdorffness, convergence, completeness etc. In addition to, we introduce fuzzy cone b-metric Banach contraction theorem using our results.

Keywords

Fuzzy metric, cone metric, cone b-metric, fuzzy cone b-metric, Banach contraction theorem, fixed point.

References

• [1] George, A. and Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(3), 395-399, (1994).
• [2] Huang and Zhang, Cone metric spaces and fixed point theorems for contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476, (2007).
• [3] Huang, L.-G. and Zhang, X., Cone metric spaces and fixed point theorems for contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476, (2007).
• [4] Hussain, N. and Shah, M., KKM mappings in cone b-metric spaces, Computers & Mathematics with Applications, 62(4), 1677-1684, (2011).
• [5] Kramosil, I. and Michálek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5), (336)-344, (1975).
• [6] Öner, T., Kandemir, M.B. and Tanay, B., Fuzzy cone metric spaces, J. Nonlinear Sci. and Appl, 8, 610-616, (2015).
• [7] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific J. Math., 10(1), 313-334, (1960).
• [8] Zadeh, L.A., Fuzzy sets, Information and Control, 8(3), 338-353, (1965).