Well-established (adjective)

1. Firmly and long established; firmly established in a desired position or condition.
2. Firmly fixed and unlikely to change.
3. Widely accepted, recognized, and acknowledged.

Origin:

Well-established is an adjective from adjective well and adjective established.

Examples:

1. The company has a well-established reputation for quality products.
2. The university has a well-established program in engineering.
3. The restaurant is a well-established favorite among locals.
4. The new law is well-established and unlikely to change anytime soon.
5. The theory is well-established in scientific community.