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No. Based upon current laws of physics/gravitation , it is not possible. All stars have masses exponentially greater than planets , therefore , stronger gravity. There may be civilizations sufficiently advanced to manufacture miniature stars to provide energy to planets deemed important for some reason , but I'll digress. Do a query on star formation , and you will learn in more detail.
To add to etacarinae's statement, if planets were to accrue more "stuff" that makes up cosmic dust, they would eventually start the fusion process and become stars themselves. Jupiter is a great example of a failed star right in our own cosmic backyard. It has so many moons that it could have easily been a little secondary star system within the larger solar system if it had been given the chance. It has 67 confirmed moons.
Alas, there wasn't enough material though and it became what it is now.
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