Could someone explain what a starlike function is?

Question

Basically I'm looking for a way to describe shapes I'm working with in a graphics analysis program and I would like to know if what I'm working with are "starlike" shapes, as in, is the boundary a starlike function.

The shapes I'm working with have a boundary which is described by a function $R(\theta)$, so for any particular angle, there is only one value of $R$. Does this mean that it is a starlike shape?

I've looked at papers about starlike functions but I can't convince myself that they are what I'm looking for.

Thanks,

With Harald's (correct) definition, it is true that the region enclosed by a polar function $R(\theta)$ together with points on the boundary is a starlike region, with central point $0$. — Jared, May 08 '13 at 18:20

score 1 · Answer 1 · answered May 08 '13 at 18:06

1

The definition of starlike region that I know of, is a region $A$ with a point $x_0$ in it so that, for any $x\in A$, the line segment between $x_0$ and $x$ lies in $A$.

answered May 08 '13 at 18:06

Harald Hanche-Olsen

31,960

1

Starlike functions? Don't know, haven't heard of them. – Harald Hanche-Olsen May 08 '13 at 18:06
A starlike region is in some way a weaker version of convexity. Maybe a starlike function is in some similar way a weaker version of a convex function? – Emily May 08 '13 at 18:49
Ok, I think that's what I was thinking, and matches the property of my shapes as far as I can see. Thanks. – user668074 May 09 '13 at 19:47

Could someone explain what a starlike function is?

1 Answers1