In mathematical writing, the term strict refers to the property of excluding equality and equivalence[1] and often occurs in the context of inequality and monotonic functions.
The opposite is non-strict, which is often understood to be the case but can be put explicitly for clarity.
In the context of functions, the adverb "strictly" is used to modify the terms "monotonic", "increasing", and "decreasing".
In the context of comparisons, one can use the phrases "non-negative", "non-positive", "non-increasing", and "non-decreasing" to make it clear that the inclusive sense of the terms is being used.
(A precise term like non-negative is never used with the word negative in the wider sense that includes zero.)