Fixed-point theorem for multivalued quasi-contraction maps in a \(V\)-fuzzy metric space. (English) Zbl 1477.54152

Summary: In this paper, we introduce the concept of a set-valued or multivalued quasi-contraction mapping in \(V\)-fuzzy metric spaces. Using this new concept, a fixed-point theorem is established. We also provide an example verifying and illustrating the fixed-point theorem in action.


54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54E40 Special maps on metric spaces
Full Text: DOI


[1] Mustafa, Z.; Sims, B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7, 2, 289-297 (2006) · Zbl 1111.54025
[2] Sedghi, S.; Shobe, N.; Aliouche, A., A generalization of fixed point theorems in s-metric spaces, Matematički Vesnik, 64, 3, 258-266 (2012) · Zbl 1289.54158
[3] Abbas, M.; Ali, B.; Suleiman, Y. I., Generalized coupled common fixed point results in partially ordered a-metric spaces, Fixed Point Theory and Applications, 2015, 1, 64 (2015) · Zbl 1314.54027
[4] Gupta, V.; Kanwar, A., V-fuzzy metric space and related fixed point theorems, Fixed Point Theory and Applications, 1, 51 (2016) · Zbl 1347.54082
[5] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 3, 338-353 (1965) · Zbl 0139.24606
[6] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64, 3, 395-399 (1994) · Zbl 0843.54014
[7] Sun, G.-P.; Yang, K., Generalized fuzzy metric spaces with properties, Research Journal of Applied Sciences, Engineering and Technology, 2, 7, 673-678 (2010)
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