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For a continuous and positive function w(λ), λ > 0 and μ a positive measure on (0, ∞) we consider the followingmonotonic integral transform

M(w,μ)(T) :=0w(λ)T(λ+T)1dμ(λ),

where the integral is assumed to exist forT a positive operator on a complex Hilbert spaceH. We show among others that, if β ≥ A, B ≥ α > 0, and 0 < δ ≤ (B − A)2 ≤ Δ for some constants α, β, δ, Δ, then




whereM(w,μ) is the second derivative ofM(w,μ) as a real function.

Applications for power function and logarithm are also provided.

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. Monoton matrices and finding cliques in a graph . Annales Univ. Sci. Budapest., Sect. Computatorica 41 ( 2013 ), 307 – 322 . [8] Weisstein , E. W . Monotonic matrix . in MathWorld–A Wolfram Web Resource .

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Authors: Ludo Waltman, Nees Jan van Eck, Thed N. van Leeuwen, Martijn S. Visser, and Anthony F. J. van Raan

in Table 4 . The Pearson correlation measures to what degree two indicators are linearly related. The Spearman correlation, on the other hand, measures to what degree two indicators are monotonically related (i.e., to what degree two indicators yield

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of parametric methods), but relies on general regularity properties, such as monotonicity, convexity, and homogeneity. DEA is based on a linear programming algorithm, constructing an efficiency frontier from data on single decision-making units (DMU

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Conference on Generalized Convexity and Monotonicity, Karlovasi, Samos, Greece, August 29 - September 2, to appear. Simonelli, I. , An Extension of the Bivariate Method of Polynomials and a Reduction Formula

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