×

On the local uniqueness of the fixed point of the probabilistic \(q\)-contraction in fuzzy metric spaces. (English) Zbl 1478.54071

Summary: In this paper we prove the local uniqueness of the fixed point of the probabilistic \(q\)-contraction in fuzzy metric space.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54E40 Special maps on metric spaces
54E70 Probabilistic metric spaces
Full Text: DOI

References:

[1] J. Acz´el, Lectures on Functional Equations and their Applications, Academic Press, New York, 1969.
[2] J. X. Fang., Onϕ-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets and Syst. 267 (2015) 86-99. · Zbl 1392.54030
[3] A. George, P. Veeramani, On some results in fuzzy metric spaces Fuzzy Sets Syst., 64 (1994), 395-399. · Zbl 0843.54014
[4] O. Hadˇzi´c, E. Pap, M. Budinˇcevi´c, On some classes of t-norms important in the fixed point theory, Kybernetika 38,3 (2002) 363-382 · Zbl 1265.54127
[5] O. Hadˇzi´c, E. Pap, On some classes of t-norms important in the fixed point theory, Bull. Acad. Serbe Sci. Art. Sci. Math. 121, 25 (2000) 15-28.
[6] O. Hadˇzi´c, E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Syst.. 127, 3 (2002) 333-344. · Zbl 1002.54025
[7] O. Hadˇzi´c, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
[8] O. Hadˇzi´c, E. Pap, Probabilistic multi-valued contractions and decomposable measures, Internat. J. Uncertainty, Fuzziness, Knowledge-Based Systems 10, Supplement (2002) 59-74. · Zbl 1060.54017
[9] O. Hadˇzi´c, E. Pap, V. Radu, Some generalized contraction mapping principles in probabilistic metric spaces, Acta Math. Hungarica 101 (1-2) (2003) 111-128.
[10] O. Kaleva, S. Seikalla, On fuzzy metric spaces, Fuzzy Sets and Syst. 12 (1984) 215-229. · Zbl 0558.54003
[11] E. P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Trends in Logic 8, Dordrecht, 2000. · Zbl 0972.03002
[12] I. Kramosil, J. Mich´alek, Fuzzy metrics and statistical metric spaces Kybernetika, 11 (1975) 336-344 · Zbl 0319.54002
[13] E. P. Klement, R. Mesiar, E. Pap, Uniform approximation of associative copulas by strict and non-strict copulas, Illinois J. Math. 45, No. 4 (2001), 1393-1400. · Zbl 1054.62064
[14] E. P. Klement, R. Mesiar, E. Pap, Archimax copulas and invariance under transformations, C. R. Math. Acad. Sci. ParisMathematics 340 (2005) 755-758. · Zbl 1126.62040
[15] K. Menger (1942). Statistical metric,Proc. Nat. Acad. USA28 (142) 535-537. · Zbl 0063.03886
[16] D. Mihet., A class of contractions in fuzzy metric spaces Fuzzy Sets Syst., 161 (2010) 1131-1137. · Zbl 1189.54035
[17] E. Pap, Null-Additive Set Functions, Kluwer Academic Publishers, Dordrecht, 1995. · Zbl 0856.28001
[18] E. Pap, O. Hadˇzi´c, R. Mesiar, A fixed point theorem in probabilistic metric spaces and applications in fuzzy set theory, J. Math. Anal. Appl. 202 (1996) 433-449. · Zbl 0855.54043
[19] V. Radu, Lectures on probabilistic analysis, Surveys, Lectures Notes and Monographs Series on Probability, Statistics & Applied Mathematics, No 2, Universitatea de Vest din Timis¸oara, 1994. · Zbl 0927.60003
[20] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Elsevier North - Holland, New York, 1983. · Zbl 0546.60010
[21] V. M. Sehgal, A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Syst. Theory 6 (1972) 97-102. · Zbl 0244.60004
[22] R. M. Tardiff, Contraction maps on probabilistic metric spaces, J. Math. Anal. Appl. 165 (1992) 517-523. · Zbl 0773.54033
[23] S. Weber,⊥-decomposable measures and integrals for Archimedean t-conorm⊥, J. Math. Anal. Appl. 101 (1984) 114-138. · Zbl 0614.28019
[24] J.Z. Xiao, X.H. Zhu, X. Jin, Fixed point theorems for nonlinear contractions in Kaleva-Seikkala’s type fuzzy metric spaces · Zbl 1260.54067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.