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Języki publikacji
Abstrakty
It is observed that in some money exchange operations, every n-variable mean M applied by two market analysts who are acting in different countries should be self reciprocally conjugate. The main result says that the only homogeneous weighted quasi-arithmetic mean satisfying this condition is the weighted geometric mean. In the context of invariance of the geometric mean with respect to the arithmetic-harmonic mean-type mapping, the possibility of the occurring reciprocal-conjugacy in technical sciences is commented.
Rocznik
Tom
Strony
5--16
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Institute of Mathematics, University of Zielona Góra, Zielona Góra, Poland
autor
- Institute of Mathematics, University of Zielona Góra, Zielona Góra, Poland
Bibliografia
- [1] Bullen, P.S. (2011). Handbook of Means and Their Inequalities. Dordrecht: Springer. DOI: 10.1007/978-94-017-0399-4.
- [2] Matkowski, J. (2020). Means, generalized harmony proportion and applications. Colloquium Mathematicum, 160(1) (2020), 109-118. DOI: 10.4064/cm7782-2-2019.
- [3] Matkowski, J. (1999), Invariant and complementary quasi-arithmetic means. Aequationes Mathematicae, 57(1), 87-107. DOI: 10.1007/s000100050072.
- [4] Daróczy, Z., & Páles, Z. (2002). Gauss-composition of means and the solution of the Matkowski-Sutô problem. Publicationes Mathematicae Debrecen, 61(1-2), 157-218. DOI:10.5486/pmd.2002.2713.
- [5] Devillet, J., & Matkowski, J. (2021). Invariance in a class of operations related to weighted quasi-geometric means. Fuzzy Sets and Systems, 414, 57-69. DOI: 10.1016/j.fss.2020.08.019.
- [6] Głazowska, D., & Matkowski, J. (2022). Generalized classical weighted means, the invariance, complementarity and convergence of iterates of the mean-type mappings. Results in Mathematics, 77(2). DOI: 10.1007/s00025-022-01608-5.
- [7] Grünwald, R., & Páles, Z. (2022). On the invariance of the arithmetic mean with respect to generalized Bajraktarevi ́c means. Acta Mathematica Hungarica, 166(2), 594-613. DOI:10.1007/s10474-022-01230-5.
- [8] Matkowski, J. (2021). Quasi-Cauchy quotients and means. Aequationes Mathematicae, 95(6), 1067-1094. DOI: 10.1007/s00010-021-00856-0.
- [9] Pasteczka, P. (2022). There is at most one continuous invariant mean. Aequationes Mathematicae, 96(4), 833-841. DOI: 10.1007/s00010-022-00870-w.
- [10] Matkowski, J., & Pasteczka, P. (2021). Mean-type mappings and invariance principle. Mathematical Inequalities & Applications, (1), 209-217. DOI: 10.7153/mia-2021-24-15.
- [11] Páles, Z., & Zakaria, A. (2018). On the invariance equation for two-variable weighted nonsymmetric Bajraktarević means. Aequationes Mathematicae, 93(1), 37-57. DOI: 10.1007/s00010-018-0560-9.
- [12] Toader, G., Costin, I., & Rassias, T.M. (2018). Means in Mathematical Analysis: Bivariate Means. London, England: Academic Press.
- [13] Hardy, G.H., Littlewood, J.E., & Pólya, G. (1952). Inequalities. Cambridge: Cambridge University Press.
- [14] Matkowski, J. (2010). Generalized weighted quasi-arithmetic means. Aequationes Mathematicae, 79(3), 203-212. DOI: 10.1007/s00010-010-0001-x.
- [15] Daróczy, Z., Páles, Z. (1987). Convexity with given infinite weight sequences. Stochastica, 11, 5-12.
- [16] Kuczma, M. (1985). An Introduction to the Theory of Functional Equations and Inequalities: Cauchy’s Equation and Jensen’s Inequality. Warszawa: Polish Scientific Editors and Silesian University.
- [17] Chudziak, J. (2020). On positive homogeneity and comonotonic additivity of the principle of equivalent utility under cumulative prospect theory. Insurance: Mathematics and Economics, 94, 154-159. DOI: 10.1016/j.insmatheco.2020.07.008.
- [18] Chudziak, J. (2022). Characterization of positive homogeneity for the principle of equivalent utility. Revista De La Real Academia De Ciencias Exactas, Físicas Y Naturales. Serie A. Matemáticas, 116(3). DOI: 10.1007/s13398-022-01269-7.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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