My answer first makes the following assumptions:
The inductor is really just a place holder for the output of a dc-dc converter (I would assume a buck converter though it doesn't matter what topology).
You're real question is how to properly decouple each of the 3 different power inputs and they power different aspects of the chip (digital and analog etc.) when the power supply is about that far or further away. You're asking about the trace layout mostly because you believe this is, in this case, important.
You have your reasons for the distance between the power supply output and the chip. Perhaps you are hoping to avoid doing that for fear of picking up noise from radiated EMI, which any switching converter will produce to some degree. And proximity is definitely your enemy when it comes to that. Regardless, I'm assuming that you asked about what to do in the situation you asked about to decouple noise, and not how to decouple something in a completely different situation like the other answers to your question.
First off, using one or 3 traces is not important in this case. You do want to minimize inductance when possible, and that is done neither by using a single common trace or 3 separate traces coming from the power output. If you have room for 3 traces, you have room for a single trace that is 3 times as wide. A single wider trace will always have lower inductance than many isolated traces. At least assuming the ground return currents are free to move in a larger plane underneath.
Once you have used this larger wide trace to reach the proximity of your chip, you must, and this is an absolute must, use local decoupling capacitors. They will be the source of power, while the larger loop will serve to recharge those capacitors, but the chip doesn't care and can't tell the difference between a distant power supply and local capacitor or the output capactor on the same supply directly adjacent. Electrons are electrons. The decoupling capacitors, well, decouple the things near by from the larger circuit by acting is local power sources. At least, in a perfect world.
But, heed the warnings about resonance and ringing. Ceramic capacitors have single digit milliohms of impedance. On inrush, they can cause large current transients and form an LC tank with just the few hundred nanohenries inductance from longer trace lengths. This is why you don't just use a ceramic capacitor.
This very real phenomenon can indeed fry or pop all sorts of semiconductors and other sensitive components, but only in improperly decoupled circuits. It's not an actual problem, as it has a very trivial and effective solution: just damp it.
There is no problem as long as you decouple your circuit properly, and properly means critically damping those LC loops.
You can do this with a series resistor (not ideal but cheap and small) or a high ESR capacitor in parallel and proximate to the ceramic decoupling capacitors. Anything above 0.5 ohms resistance (in series or the ESR to ground of a capacitor) will prevent any voltage overshoot from occurring even for meter long traces. Tantalums (non polymer) are great for this, they typically have 1 or two ohms resistance and are small.
So, use a single wide trace, fan it out at the chip with a separate ceramic decoupling capacitor for each supply rail, all connected to the same positiv terminal of a high ESR electrolytic (aluminum or tantalum) and you'll be fine.
http://cds.linear.com/docs/en/application-note/an88f.pdf goes into this with more depth for anyone interested.