Some Theorems on the Demeanour of Probabilistic Uncertainty-Like Functional under the Bounds
Asian Journal of Probability and Statistics,
Page 200-207
DOI:
10.9734/ajpas/2022/v20i4449
Abstract
The resulting mean of the optimal solutions of minimization problems, whose objective functions are the uncertainty like functionals, are known as uncertainty mean. The uncertainty mean satisfies all the basic properties of the classical mean, weighted homogeneous mean as well as many others are special cases of uncertainty mean. The indeed paper deals with comparison property and asymptotic demeanour of the uncertainty mean.
Keywords:
- Uncertainty mean
- uncertainty like functional
- comparison theorem
- asymptotic demeanour
- weighted mean
- homogeneous mean etc
How to Cite
Verma, R. K. (2022). Some Theorems on the Demeanour of Probabilistic Uncertainty-Like Functional under the Bounds. Asian Journal of Probability and Statistics, 20(4), 200-207. https://doi.org/10.9734/ajpas/2022/v20i4449
References
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Bullen PS, Mitrinovic DS, Vasic PM. Means and their inequalities. Princeton Series in Applied Mathematics. 2007;Chapters 4-6.
Bodenhofer U. Representations and constructions of similarity-based fuzzy orderings. Fuzzy Sets and Systems. 2003;137(1):113-136.
Matkowski J. Iterations of the mean-type mappings and uniqueness of invariant means. Annales Univ. Sci. Budapest, Sect. Comp. 2013;41:145-158.
Mercer PR. Cauchy’s mean value theorem meets the logarithmic mean. Math. Gaz. 2017;101(550):108-115.
Kapur JN. Measures of information and their applications. Wiley Eastern, New Delhi; 1997.
Bhatia R, Holbrook J. Non-commutative geometric mean. Mathematical Intelligencer. 2006;28:32-39.
Chakraborty S. A short note on the versatile power mean. Resonance. 2007;12(9):76-79.
Zou L, Jiang Y. Improved arithmetic-geometric mean Inequality and its application. J. Math. Ineq. 2015;9(1):107-111.
Carlson BC. The logarithm mean. M.A.A. Monthly. 1972;79:615-618.
Brenner JL, Carlson BC. Homogeneous mean values: Weights and asymptotics. J. Math. Anal. Appl. 1987;123:265-280.
Borwein JM, Borwein PB. Pi, AGM. A study in analytic number theory and computational complexity. “Canadian Mathematical Society Series of Monographs”, Wiley-Interscience, New York; 1987.
Bullen PS, Mitrinovic DS, Vasic PM. Means and their inequalities. Princeton Series in Applied Mathematics. 2007;Chapters 4-6.
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