Tagged Questions
2
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0answers
173 views
Jensen's Inequality for complex functions
Jensen's inequality states that if $\mu$ is a probability measure on $X$, $\phi$ is convex, and $f$ is a real-valued function, then
$$ \int \phi(f) \, d\mu \geq \phi\left(\int f \, d\mu\right).$$
Is ...
1
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1answer
111 views
How to show it is convex?
From a journal entitled Certain subclass of starlike functions by Gao and Zhou in 2007, they mentioned that " since $ k(z)=\frac{z}{1-zt}$ is convex in open unit disk $E,z:|z|<1$, $k(\bar{z})= ...
1
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0answers
68 views
Solution for this Convolution
We have $f(z)=z+ \sum_{n=2}^{\infty} a_{n}z^{n}$ where $a_{n}$ is a constant and $g(z)=z$, $(f*g)(z)$ is equal to what? i still wondering to confirm that $(f*g)(z)=z$.
1
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1answer
88 views
Can this equality be proved?
I get the additional $+1$ in the RHS of this equality. Did you can prove this?
$\frac{-(|p(z)-1|^{2}-r^{2}|p(z)+1|^{2})}{4(1-r^{2})|p(z)+h|}=\frac{-|p(z)|^{2}+2(1+r^{2})Re (p(z))}{4|p(z)+h|}$
noted ...
2
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2answers
242 views
Example of Convex Function
Knowning that $f(z)=z+a_2z^2+a_3z^3+...$ is a convex function, is it the derivative of f(z) is also a convex function?
