Abstract
The notion of strongly Schur-convex functions is introduced and functions generating strongly Schur-convex sums are investigated. The results presented are counterparts of the classical Hardy–Littlewood–Pólya majorization theorem and the theorem of Ng characterizing functions generating Schur-convex sums. It is proved, among others, that for some (for every) n≥2, the function F(x 1,…,x n)=f(x 1)+⋯+f(x n) is strongly Schur-convex with modulus c if and only if f is of the form f(x)=g(x)+a(x)+c∥x∥2, where g is convex and a is additive.
Keywords
- Schur-convex functions
- Strongly Schur-convex functions
- Strongly convex functions
- Strongly Jensen-convex functions
- Strongly Wright-convex functions
- Doubly stochastic matrices
- Majorization
Mathematics Subject Classification
The research of the third author was supported by the University of Bielsko-Biała internal grant No. 08/II/GW/2009.
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Dedicated to the Memory of Professor Wolfgang Walter
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Nikodem, K., Rajba, T., Wąsowicz, S. (2012). Functions Generating Strongly Schur-Convex Sums. In: Bandle, C., Gilányi, A., Losonczi, L., Plum, M. (eds) Inequalities and Applications 2010. International Series of Numerical Mathematics, vol 161. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0249-9_13
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DOI: https://doi.org/10.1007/978-3-0348-0249-9_13
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