Difference between revisions of "Diamond alpha derivative"
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| + | [http://arxiv.org/pdf/0902.1380%20%5Bmath.CA%5D]<br /> | ||
Revision as of 08:23, 12 April 2015
Properties
Theorem: Let $0 \leq \alpha \leq 1$. If $f$ is both $\Delta$ and $\nabla$ differentiable at $t \in \mathbb{T}$ then $f$ is $\Diamond_{\alpha}$-differentiable at t and $$f^{\Diamond_{\alpha}}(t)=\alpha f^{\Delta}(t) + (1-\alpha)f^{\nabla}(t).$$
Proof: █
