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

where the integral is assumed to exist for*T* a positive operator on a complex Hilbert space*H*. 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

and

where

Applications for power function and logarithm are also provided.

. 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 .

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

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

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