Results 301 to 310 of about 312,373 (317)
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Weighted Inequalities for Monotone Functions
Mathematische Nachrichten, 1995AbstractWeighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi‐linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which \documentclass{article}\pagestyle{empty}
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1990
The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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Bessel Functions: Monotonicity and Bounds
Journal of the London Mathematical Society, 2000The aim of this paper is the derivation of monotonicity properties of Bessel functions, leading to precise bounds which are uniform in order or argument. Monotonicity with respect to the order \(\nu\) of the magnitude of general Bessel functions. \({\mathcal C}_\nu(x)= aJ_\nu(x)+ bY_\nu(x)\) at positive stationary points of associated functions is ...
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Elements of Monotonic Analysis: Monotonic Functions
2000The theory of IPH functions defined on either the cone ℝ ++ n or the cone ℝ + n can be applied in the study of various classes of monotonic functions. One of possible approaches in this direction is to use the hypographs of decreasing functions and the epigraphs of increasing functions.
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On a Singular Monotone Function
Journal of the London Mathematical Society, 1937van Kampen, E. R., Wintner, Aurel
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The Structure of Monotone Functions
American Journal of Mathematics, 1937Hartman, Philip, Kershner, Richard
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The Stolarsky type functions and their monotonicities
2009Summary: We give the definition of a Stolarsky type function, and obtain its monotonicity. By using these results, we establish a series of means and their monotonicities in \(n\) variables.
LOKESHA, V. +3 more
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