Geodesic
Suzuki type fuzzy $\mathcal {Z}$-contractive mappings and fixed points in fuzzy metric spaces
Kybernetika, Tome 57 (2021) no. 6, pp. 908-921
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In this paper, we propose the concept of Suzuki type fuzzy $\mathcal{Z}$-contractive mappings, which is a generalization of Fuzzy $\mathcal{Z}$-contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in $G$-complete as well as $M$-complete fuzzy metric spaces. A comprehensive set of examples are furnished to demonstrate the validity of the obtained results.
In this paper, we propose the concept of Suzuki type fuzzy $\mathcal{Z}$-contractive mappings, which is a generalization of Fuzzy $\mathcal{Z}$-contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in $G$-complete as well as $M$-complete fuzzy metric spaces. A comprehensive set of examples are furnished to demonstrate the validity of the obtained results.
DOI : 10.14736/kyb-2021-6-0908
Classification : 47H10, 54H25
Keywords: fuzzy metric space; fuzzy $\mathcal {Z}$-contractive mapping; Suzuki type fuzzy $\mathcal {Z}$-contractive mappings; fixed point 
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Gopal, Dhananjay; Martínez-Moreno, Juan. Suzuki type fuzzy $\mathcal {Z}$-contractive mappings and fixed points in fuzzy metric spaces. Kybernetika, Tome 57 (2021) no. 6, pp. 908-921. doi: 10.14736/kyb-2021-6-0908

[1] Altun, I., Mihet, D.: Ordered Non-Archimedean fuzzy metric spaces and some fixed point results. Fixed Point Theory Appl. 2010 (2010), Article ID 782680. | DOI | MR

[2] George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets and Systems 64 (1994), 395-399. | DOI | MR | Zbl

[3] Gopal, D., Abbas, M., Imdad, M.: $\psi$-weak contractions in fuzzy metric spaces. Iranian Journal of Fuzzy Systems 8(5) (2011), 141-148. | MR

[4] Gopal, D., Vetro, C.: Some new fixed point theorems in fuzzy metric spaces. Iranian J. Fuzzy Systems 11 (2014), 3, 95-107. | MR

[5] Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 27 (1988), 385-389. | DOI | MR | Zbl

[6] Gregori, V., Sapena, A.: On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets and Systems 125 (2002), 245-252. | DOI | MR

[7] Gregori, V., Miñana, J-J.: Some remarks on fuzzy contractive mappings. Fuzzy Sets and Systems 251 (2014), 101-103. | DOI | MR

[8] Gregori, V., Miñana, J-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets and Systems 204 (2012), 71-85. | DOI | MR | Zbl

[9] Gregori, V., Miñana, J-J.: On fuzzy $\psi$-contractive mappings. Fuzzy Sets and Systems 300 (2016), 93-101. | DOI | MR

[10] Hadžić, O., Pap, E.: Fixed Point Theory in PM-spaces. Kluwer Academic Publishers, Dordrecht 2001. | MR

[11] Kramosil, I., Michálek, J.: Fuzzy metric and statistical metric spaces. Kybernetica 15 (1975), 326-334. | DOI | MR

[12] Miheţ, D.: Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems 159 (2008), 739-744. | DOI | MR

[13] Miheţ, D.: A class of contractions in fuzzy metric spaces. Fuzzy Sets and Systems 161 (2010), 1131-1137. | DOI | MR

[14] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. Elsevier, New York 1983. | MR | Zbl

[15] Shukla, S., Gopal, D., Rodríguez-López, R.: Fuzzy-Prešić-Ćirić operators and applications to certain nonlinear differential equations. Math. Modell. Anal. 21 (2016), 6, 11-835. | DOI | MR

[16] Shukla, S., Gopal, D., Sintunavarat, W.: A new class of fuzzy contractive mappings and fixed point theorems. Fuzzy Sets and Systems 350 (2018), 85-95. | DOI | MR

[17] Suzuki, T.: A generalized Banach contraction principle which characterizes metric completeness. Proc. Amer. Math. Soc. 136 (2008), 5, 1861-1869. | DOI | MR

[18] Tirado, P.: On compactness and $G$-completeness in fuzzy metric spaces. Iranian J. Fuzzy Systems 9 (2012), 4, 151-158. | MR

[19] Vasuki, R., Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets and Systems 135 (2003), 415-417. | DOI | MR

[20] Wardowski, D.: Fuzzy contractive mappings and fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 222 (2013), 108-114. | DOI | MR

[21] Zheng, D., Wang, P.: Meir-Keeler theorems in fuzzy metric spaces. Fuzzy Sets and Systems 370 (2019), 120-128. | DOI | MR

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