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A class of contractions in fuzzy metric spaces. (English) Zbl 1189.54035
Summary: Using the notion of geometrically convergent t-norms, a fixed point theorem in fuzzy metric spaces in the sense of Kramosil and Michalek for a class of contractions, larger than the class of $(\varepsilon ,\lambda )$-contraction mappings, has been proved.

54H25Fixed-point and coincidence theorems in topological spaces
54E70Probabilistic metric spaces
Full Text: DOI
[1] Deng, Zi-Ke: Fuzzy pseudo-metric spaces, J. math. Anal. appl. 86, 74-95 (1982) · Zbl 0501.54003 · doi:10.1016/0022-247X(82)90255-4
[2] George, A.; Veeramani, P.: On some results in fuzzy metric spaces, Fuzzy sets and systems 64, 35-39 (1994) · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[3] Gregori, V.; Sapena, A.: On fixed point theorems in fuzzy metric spaces, Fuzzy sets and systems 125, 245-252 (2002) · Zbl 0995.54046 · doi:10.1016/S0165-0114(00)00088-9
[4] Hadžić, O.; Budinčević, M.: A fixed point theorem in PM spaces, Colloq. math. Soc. J. Bolyai 23, 569-579 (1978)
[5] Hadžić, O.; Pap, E.: Fixed point theory in probabilistic metric spaces, (2001)
[6] Hadžić, O.; Pap, E.; Budinčević, M.: Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetika 38, No. 3, 363-381 (2002) · Zbl 1265.54127
[7] Hadžić, O.; Pap, E.; Budinčević, M.: A generalization of tardiff’s fixed point theorem in probabilistic metric spaces and applications to random equations, Fuzzy sets and systems 156, 124-134 (2005) · Zbl 1086.54018 · doi:10.1016/j.fss.2005.04.007
[8] Hadžić, O.; Pap, E.: Fixed point theorems for single-valued and multivalued mappings in probabilistic metric spaces, Atti sem. Mat. fiz. Modena Li, 377-395 (2003) · Zbl 1259.54020
[9] Hadžić, O.; Pap, E.: New classes of probabilistic contractions and applications to random operators, Fixed point theory and application 4, 97-119 (2003) · Zbl 1069.54026
[10] Kaleva, O.; Seikkala, S.: On fuzzy metric spaces, Fuzzy sets and systems 12, 215-229 (1984) · Zbl 0558.54003 · doi:10.1016/0165-0114(84)90069-1
[11] Kramosil, I.; Michalek, J.: Fuzzy metrics and statistical metric spaces, Kybernetika 11, 336-344 (1975) · Zbl 0319.54002
[12] Miheţ, D.: A class of sehgal’s contractions in probabilistic metric spaces, An. univ. Vest timisoara ser. Mat. informatica 37, 105-110 (1999) · Zbl 0997.54048
[13] Miheţ, D.: A Banach contraction theorem in fuzzy metric spaces, Fuzzy sets and systems 144, 431-439 (2004) · Zbl 1052.54010 · doi:10.1016/S0165-0114(03)00305-1
[14] Miheţ, D.: On the existence and the uniqueness of fixed points of sehgal contractions, Fuzzy sets and systems 156, 135-141 (2005) · Zbl 1082.54022 · doi:10.1016/j.fss.2005.05.024
[15] Miheţ, D.: Multivalued generalizations of probabilistic contractions, J. math. Anal. appl. 304, 464-472 (2005) · Zbl 1072.47066 · doi:10.1016/j.jmaa.2004.09.034
[16] Miheţ, D.: A note on a paper of hadžić and pap, Fixed point theory and applications 7, 127-133 (2007)
[17] V. Radu, Some Fixed Point Theorems in PM Spaces, in: Lectures Notes in Mathematics, Vol. 1233, 1987, pp. 125 -- 133.
[18] V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, in: The 8-th Internat. Conf. on Applied Mathematics and Computer Science, Cluj-Napoca, 2002, Automat. Comput. Appl. Math. 11 (2002) 125 -- 131.
[19] Schweizer, B.; Sklar, A.: Probabilistic metric spaces, (1983) · Zbl 0546.60010
[20] Schweizer, B.; Sherwood, H.; Tardif, R. M.: Contractions on PM-spaces: examples and counterexamples, Stochastica 12, No. 1, 5-17 (1988) · Zbl 0689.60019
[21] S. Sedghi, T. Žikić-Došenović, N. Shobe, Common fixed point theorems in Menger probabilistic quasimetric spaces, in: Fixed Point Theory and Applications, Vol. 2009, 2009, Article ID 546273, doi:10.1155/2009/546273. · Zbl 1171.54035 · doi:10.1155/2009/546273
[22] Sehgal, V. M.; Bharucha-Reid, A. T.: Fixed points of contraction mappings on PM-spaces, Math. syst. Theory 6, 97-100 (1972) · Zbl 0244.60004 · doi:10.1007/BF01706080
[23] Sherwood, H.: Complete probabilistic metric spaces, Wahr. verw. Geb. 20, 117-128 (1971) · Zbl 0212.19304 · doi:10.1007/BF00536289
[24] P. Tirado, Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets, in: VII Iberoamerican Conf. on Topology and its Applications, Valencia, Spain, 25 -- 28 June 2008.
[25] Žikić, T.: On fixed point theorems of gregori and sapena, Fuzzy sets and systems 144, No. 3, 421-429 (2004) · Zbl 1052.54006 · doi:10.1016/S0165-0114(03)00179-9