Can someone please help me to prove the following inequality: let $a,b$ be any two complex numbers and $p>1$ we have $\left||a|^{p-1}a-|b|^{p-1} b\right|\leq c\left(|a|^{p-1} +|b|^{p-1}\right)|a-b|$ where $c$ is a constant that depends on $p$. Thanks
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I edited your question pretty thoroughly: check that the end result matches the question you had in mind. – DylanSp Mar 09 '16 at 15:49
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i will use this inegality to prove that the solution of schrodinger equation is unique – Mar 09 '16 at 15:58
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i only wrote $||a|^{p-1}a-|b|^{p-1} b|$<$|a|^p+|b|^p$ and i am blocked there – Mar 09 '16 at 16:39
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proving the inegality is equivalent to prove that $|1-t^p e^{i \varphi} | \leq c(1+t^{p-1}) |1-t e^{i \varphi}|$ but i don't know how to prove thatcan someone help – Mar 09 '16 at 20:48
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On a simulation basis, this constant looks to be $p/2$. Interesting ! – Jean Marie Mar 09 '16 at 21:40