There is only one Disneyland, yet there are many, many amusement and theme parks. There is only one Kleenex, yet many, many brands of tissues. There is only one Amazon.com, yet there are many, many, online sellers of books. And so it goes on.
When you think of competition and the possibility of them taking your place, it is not that they are better, cheaper or larger, it is that you have not carved out your place in a unique way. Think of Disneyland. They have lots of rides, yet none compare to the rides at some of the Six Flags parks, and others around the country. Yet it is their uniqueness that keeps people coming back again and again. I've been to the one in LA at least 12 times myself, yet other amusement parks are not even on the radar screen.
I like to say that there is no competition--and, I believe it. No one can come and take away what is mine without my permission. It is so easy to carve out your own niche and uniqueness that no one can match. We could even call it personality to make it a human element. There are no two people exactly alike--each is unique, no matter how similar some may seem. That applies to twins. They look alike, yet they are not at all.
If you think of competition, you are thinking with a lack mentality; i.e., there is only so much to go around--so many customers, so much product, so many opportunities, etc. It will be that thinking that will cause you to lose your place. If, on the other hand, you think with an abundance mentality, there will always be enough for everyone, no matter how many there are. It is a challenge to think that way if you watch the news, read the paper, listen to lack thinkers, but the more you do it, the easier it is and you will find that will be your truth. You get to choose your truth. William Shakespeare said it so well a long time ago: ". . . there is nothing either good or bad, but thinking makes it so."
Delete competition from your mind. You are in charge of your own destiny! Go for it and make it your own.