The phrase "a fixed idea of" is correct and usable in written English.
It can be used to describe a strong, unchanging belief or concept that someone holds about something or someone.
Example: "She has a fixed idea of what success looks like, and she is unwilling to consider alternative definitions."
Alternatives: "a rigid notion of" or "an unchanging perception of".
There's a fixed idea of what foreign journalists visiting Tehran can expect.
"I never knew people had a fixed idea of who I was, or that I even had a fanbase, until everyone was surprised about Pineapple Express.
Giorgio Armani's trouble is that he has a fixed idea of couture: all taut lines and sweetheart bodices trimmed out like a chocolate box.
They bring with them a fixed idea of what a university is all about, and are unexcited by what they consider their chancellor's unglamorous goal.
"Very often a fanbase has a fixed idea of how they want to see their songs presented, but the problem with Viva Forever! is that the songs didn't really lend themselves to the musical context of the story".
This suggests that most of us don't have a fixed idea of how much we want; instead, we look to outside cues like the size of a package or cup to instruct us.
Of course his music and poetry stand alone in their magnificence, but his refusal to conform to any fixed idea of who he is as an artist seems to me a kind of living metaphor for the nature of life and human identity itself.
The set-up of the urbanism focus group varies greatly from one enterprise to another, but to get a fixed idea, a team of between two and eight people can fulfill all the missions of an urbanism focus group as described in this chapter.
"There's a very fixed idea of what an apartment needs to be", she said.
He did not begin with a fixed idea about the form of functions, and so the operations he developed were quite general.
"If you come in with a very fixed idea of what you want, then you are going to struggle," says Hubbard. "Because the nature of the beast is that you keep having to give way and find an alternative way of getting there".
