Common tripled fixed point theorem for W-compatible mappings in fuzzy metric spaces

Volume 9, Issue 3, pp 806--818 Publication Date: March 25, 2016
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Authors

Jing-Feng Tian - College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, P. R. China. Xi-Mei Hu - China Mobile Group Hebei Co., Ltd., Baoding, Hebei Province, 071000, P. R. China. Hong-Shan Zhao - School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei Province, 071003, P. R. China.

Abstract

In this paper we present a common tripled fixed point theorem for W-compatible mappings under $\phi$- contractive conditions in fuzzy metric spaces. The result generalizes, extends and improves several classical and very recent related results in literature. For instance, we obtain an extension of Theorem 2.5 in [S. Sedghi, I. Altun, N. Shobe, Nonlinear Anal., 72 (2010), 1298-1304], an refinement of Theorem 4.1 in [X. Zhu, J. Xiao, Nonlinear Anal., 74 (2011), 5475-5479] and an improvement of Theorem 11 in [A. Roldán, J. Martínez-Moreno, C. Roldán, Fixed Point Theory Appl., 2013 (2013), 13 pages]. Finally, an example is given to illustrate the usability of our main result.

Keywords

• Common tripled fixed point
• tripled fixed point
• fuzzy metric space
• Hadžić type t-norm.

•  47H10

References

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