zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Probabilistic (quasi)metric versions for a stability result of Baker. (English) Zbl 1259.39022
Summary: By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in random normed spaces.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
46S50Functional analysis in probabilistic metric linear spaces
WorldCat.org
Full Text: DOI
References:
[1] J. A. Baker, “The stability of certain functional equations,” Proceedings of the American Mathematical Society, vol. 112, no. 3, pp. 729-732, 1991. · Zbl 0735.39004 · doi:10.2307/2048695
[2] V. Radu, “The fixed point alternative and the stability of functional equations,” Fixed Point Theory, vol. 4, no. 1, pp. 91-96, 2003. · Zbl 1051.39031
[3] L. C\uadariu and V. Radu, “Fixed points and the stability of Jensen’s functional equation,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, 7 pages, 2003. · Zbl 1043.39010 · emis:journals/JIPAM/v4n1/index.html · eudml:123714
[4] D. Mihe\ct and V. Radu, “On the stability of the additive Cauchy functional equation in random normed spaces,” Journal of Mathematical Analysis and Applications, vol. 343, no. 1, pp. 567-572, 2008. · Zbl 1139.39040 · doi:10.1016/j.jmaa.2008.01.100
[5] D. Mihe\ct, “The fixed point method for fuzzy stability of the Jensen functional equation,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1663-1667, 2009. · Zbl 1179.39039 · doi:10.1016/j.fss.2008.06.014
[6] A. K. Mirmostafaee, “A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1653-1662, 2009. · Zbl 1187.46067 · doi:10.1016/j.fss.2009.01.011
[7] D. Mihe\ct, “The probabilistic stability for a functional nonlinear equation in a single variable,” Journal of Mathematical Inequalities, vol. 3, no. 3, pp. 475-483, 2009. · Zbl 1187.39044 · doi:10.7153/jmi-03-47 · http://files.ele-math.com/abstracts/jmi-03-47-abs.pdf
[8] M. E. Gordji and H. Khodaei, “The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 140767, 15 pages, 2010. · Zbl 1221.39036 · doi:10.1155/2010/140767 · eudml:232111
[9] H. A. Kenary and Y. J. Cho, “Stability of mixed additive-quadratic Jensen type functional equation in various spaces,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2704-2724, 2011. · Zbl 1235.39024 · doi:10.1016/j.camwa.2011.03.024
[10] C. Park, J. R. Lee, and D. Y. Shin, “Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation,” Applied Mathematics Letters, vol. 25, no. 2, pp. 200-205, 2012. · Zbl 1238.39012 · doi:10.1016/j.aml.2011.08.018
[11] A. Ebadian, M. Eshaghi Gordji, H. Khodaei, R. Saadati, and Gh. Sadeghi, “On the stability of an m-variables functional equation in random normed spaces via fixed point method,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 346561, 13 pages, 2012. · Zbl 1244.39022 · doi:10.1155/2012/346561
[12] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing, New York, 1983. · Zbl 0546.60010
[13] O. Had\vzić, “On the (\epsilon ,\lambda )-topology of probabilistic locally convex spaces,” Glasnik Matemati\vcki III, vol. 13, no. 33, pp. 293-297, 1978. · Zbl 0403.46001
[14] O. Had\vzić and M. Budincevic, “A fixed point theorem in PM spaces,” Colloquia Mathematica Societatis Janos Bolyai, vol. 23, pp. 569-579, 1978.
[15] V. Radu, “On the t-norms of the Had\vzić type and fixed points in probabilistic metric spaces,” Review of Research, vol. 13, pp. 81-85, 1983. · Zbl 0586.47063
[16] V. M. Sehgal and A. T. Bharucha-Reid, “Fixed points of contraction mappings on probabilistic metric spaces,” Mathematical Systems Theory, vol. 6, pp. 97-102, 1972. · Zbl 0244.60004 · doi:10.1007/BF01706080
[17] O. Had\vzić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
[18] D. Mihe\ct, “The probabilistic stability for a functional equation in a single variable,” Acta Mathematica Hungarica, vol. 123, no. 3, pp. 249-256, 2009. · Zbl 1212.39036 · doi:10.1007/s10474-008-8101-y
[19] Y. J. Cho, M. Grabiec, and V. Radu, On Nonsymmetric Topological and Probabilistic Structures, Nova Science Publishers, New York, NY, USA, 2006. · Zbl 1219.54001
[20] D. Mihe\ct, “A note on a fixed point theorem in Menger probabilistic quasi-metric spaces,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2349-2352, 2009. · Zbl 1198.54081 · doi:10.1016/j.chaos.2007.10.029