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Integral means of harmonic mappings
1998Summary: We prove that if \(f\) is a univalent, sense-preserving, harmonic mapping of the unit disc onto the symmetric strip \(|\Im w|
Grigoryan, Armen, Nowak, Maria (1951- )
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Illumination Harmonization with Gray Mean Scale
2020Illumination harmonization is an important problem for high-quality image composite. Given the source image and the target background, it aims to transform the foreground appearance that it looks in the same lighting condition as the target background.
Shuangbing Song +3 more
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Harmonic, Logarithmic, and Arithmetic Means and Corollaries
The American Mathematical Monthly, 2020For two positive real numbers a and b, their harmonic, logarithmic, and arithmetic means are respectively defined by H(a,b)=21a+1b=2aba+b,L(a,b)=b−a ln b− ln a , and A(a,b)=a+b2 .Theorem.
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The Arithmetic-Harmonic mean and Landen transformations
2019An elementary transformation on the coefficients of a rational function of degree 2, preserving the value of its integral, is presented.
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A Harmonic Mean Inequality for the Gamma Function
SIAM Journal on Mathematical Analysis, 1974We prove that the harmonic mean of $\Gamma (x)$ and $\Gamma (1/ x)$ is greater than or equal to $\Gamma (1) = 1$ for arbitrary $x > 0$.
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Approximation in the mean by harmonic functions
Journal of Soviet Mathematics, 1975Maz'ya, V. G., Khavin, V. P.
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