Geodesic
Some fixed point theorems for $\varphi$-contractive mappings in fuzzy normed linear spaces :
Nădăban, Sorin 1   ; Bînzar, Tudor 2   ; Pater, Flavius 2
1 Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330, Arad, Romania
2 Department of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, Romania
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5668-5676 Cet article a éte moissonné depuis la source International Scientific Research Publications

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In this paper a new concept of comparison function is introduced and discussed and some fixed point theorems are established for $\varphi$-contractive mappings in fuzzy normed linear spaces. In this way we obtain fuzzy versions of some classical fixed point theorems such as Nemytzki-Edelstein's theorem and Maia's theorem.

DOI : 10.22436/jnsa.010.11.05
Classification : 46S40
Keywords: Fuzzy normed linear spaces, \(\varphi\)-contractive mappings, fixed point theorems

Nădăban, Sorin  1   ; Bînzar, Tudor  2   ; Pater, Flavius   2

1 Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330, Arad, Romania
2 Department of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, Romania 
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Nădăban, Sorin; Bînzar, Tudor; Pater, Flavius . Some fixed point theorems for \(\varphi\)-contractive mappings in fuzzy normed linear spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5668-5676. doi: 10.22436/jnsa.010.11.05

[1] Alegre, C.; Romaguera, S. Characterizations of fuzzy metrizable topological vector spaces and their asymmetric generalization in terms of fuzzy (quasi-)norms, Fuzzy Sets and Systems, Volume 161 (2010), pp. 2181-2192 | DOI

[2] Altun, I.; Miheţ, D. Ordered non-archimedean fuzzy metric spaces and some fixed point results, Fixed Point Theory and Appl., Volume 2010 (2010), pp. 1-11 | DOI | Zbl

[3] Bag, T.; Samanta, S. K. Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., Volume 11 (2003), pp. 687-705

[4] Bag, T.; Samanta, S. K. Fuzzy bounded linear operators, Fuzzy Sets and Systems, Volume 151 (2005), pp. 513-547 | DOI

[5] Bag, T.; Samanta, S. K. Fixed point theorems on fuzzy normed linear spaces, Inform. Sci., Volume 176 (2006), pp. 2910-2931 | DOI

[6] Bag, T.; Samanta, S. K. Some fixed point theorems in fuzzy normed linear spaces, Inform. Sci., Volume 177 (2007), pp. 3271-3289 | DOI

[7] Berinde, V. Iterative Approximation of Fixed Points, Springer, Berlin, 2007 | DOI

[8] Bînzar, T.; Pater, F.; Nădăban, S. On fuzzy normed algebras, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 5488-5496 | Zbl | DOI

[9] Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl., Volume 24 (1968), pp. 182-190

[10] Cheng, S. C.; J. N. Mordeson Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., Volume 86 (1994), pp. 429-436

[11] Y. J. Cho Fixed points in fuzzy metric spaces, J. Fuzzy Math., Volume 5 (1997), pp. 949-962

[12] I. Dzitac The fuzzification of classical structures: A general view, Int. J. Comput. Commun. Control, Volume 10 (2015), pp. 12-28

[13] Fang, J. X. On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 46 (1992), pp. 107-113 | DOI

[14] C. Felbin Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems, Volume 48 (1992), pp. 239-248 | DOI

[15] George, A.; P. Veeramani On some results in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 64 (1994), pp. 395-399 | DOI

[16] I. Goleţ On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy Sets and Systems, Volume 161 (2010), pp. 1138-1144 | DOI

[17] Grabiec, M. Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 27 (1988), pp. 385-389 | DOI

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

[19] Hadžić, O.; Pap, E. Fixed point theory in probabilistic metric spaces, Kluwer Academic Publishers, Dordrecht, 2001

[20] A. K. Katsaras Fuzzy topological vector spaces II, Fuzzy Sets and Systems, Volume 12 (1984), pp. 143-154 | DOI

[21] E. E. Kerre The impact of fuzzy set theory on contemporary mathematics: survey, Appl. Comput. Math., Volume 10 (2011), pp. 20-34 | Zbl

[22] Nădăban, S.; Dzitac, I. Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications, Informatica, Volume 25 (2014), pp. 643-662 | Zbl | DOI

[23] Plebaniak, R. New generalized fuzzy metrics and fixed point theorem in fuzzy metric space, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-17 | Zbl | DOI

[24] Rosenfeld, A. Fuzzy groups, J. Math. Anal. Appl., Volume 35 (1971), pp. 512-517

[25] I. A. Rus Generalized Contractions and Applications, Cluj University Press, Romania, 2001

[26] Saadati, R.; Kumam, P.; Jang, S. Y. On the tripled fixed point and tripled coincidence point theorems in fuzzy normed spaces, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-16 | DOI | Zbl

[27] Saadati, R.; Vaezpour, S. M. Some results on fuzzy Banach spaces, J. Appl. Math. Comput., Volume 17 (2005), pp. 475-484 | DOI

[28] Sadeqi, I.; F. S. Kia Fuzzy normed linear space and its topological structure, Chaos Solitons Fractals, Volume 40 (2009), pp. 2576-2589 | DOI

[29] Schweizer, B.; Sklar, A. Statistical metric spaces, Pacific J. Math., Volume 10 (1960), pp. 314-334

[30] Xiao, J.-Z.; Zhu, X.-H. Topological degree theory and fixed point theorems in fuzzy normed spaces, Fuzzy Sets and Systems, Volume 147 (2004), pp. 437-452 | DOI | Zbl

[31] Zadeh, L. A. Fuzzy sets , Information and Control, Volume 8 (1965), pp. 338-353

[32] Zhu, J.; Wang, Y.; Zhu, C.-C. Fixed point theorems for contractions in fuzzy normed spaces and intuitionistic fuzzy normed spaces, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-10 | Zbl | DOI

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