Fixed Point Theorems for kg- Contractive Mappings in a Complete Strong Fuzzy Metric Space

Document Type: Original Scientific Paper

Authors

1 Mathematics, College Of Science and Technology Andhra University, Visakhapatnam, Andhra Pradesh, India

2 Mathematics, College of Science and Technology, Andhra University

Abstract

In this paper, we introduce a new class of contractive mappings in a fuzzy metric space and we present fixed point results for this class of maps.

Keywords

Main Subjects


1. A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994) 395–399.

2. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27(3) (1988) 385–389.

3. V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115(3) (2000) 485–489.

4. V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems Vol. 125, Issue 2, 2002, 245–252.

5. V. Gregori, A. Sapena, Remarks to “On strong intuitionistic fuzzy metrics", submitted to J. Nonlinear Sci. Appl..

6. J. Gutiérrez García, S. Romaguera, Examples of non-strong fuzzy metrics, Fuzzy Sets and Systems 162(1)(2011) 91–93.

7. I. Kramosil, J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika 11(5) (1975) 336–344.

8. D. MiheŇ£, A class of contractions in fuzzy metric spaces, Fuzzy Sets and Systems 161(8) (2010) 1131–1137.

9. S. Phiangsungnoen, Y. J. Cho, P. Kumam, Fixed point results for modified various contractions in fuzzy metric spaces via α-admissible, Filomat 30(7) (2016) 1869–1881.

10. J. Rodríguez-López, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147(2) (2004) 273–283.

11. A. Sapena, S. Morillas, On strong fuzzy metrics, In: Proceedings of the Workshop in Applied Topology WiAT’09 (2009) 135–141.

12. B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960) 313–334.

13. S. L. Singh, R. Kamal, M. De la Sen, R. Chugh, A fixed point theorem for generalized weak contractions, Filomat 29(7) (2015) 1481–1490.