Strictly monotonically increasing

Japanese: 狭義単調増加 - きょうぎたんちょうぞうか

...Increasing and decreasing functions are collectively called monotonic functions. In particular, when f ( _x1 )< f ( x2 ) or f ( x1 ₎ > f (x2) for as long as x1<x2, f(x ₎ _is said _to be strictly monotonically _increasing or decreasing, respectively, and these cases are collectively called strictly monotonic. The monotonicity of a function can also be described for a portion of its domain. ...

From [Differentiation]

...If f ′( x ) ≧ 0 in a given interval, then f ( x ) is monotonically increasing in that interval. In particular, if f ′( x ) ＞ 0 is always true in that interval, then f ( x ) is strictly monotonically increasing. Also, if f ′( x ) ≦ 0 in a given interval, then f ( x ) is monotonically decreasing in that interval. ...

*Some of the terminology explanations that mention "strictly monotonically increasing" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…増加関数と減少関数とを総称して単調関数という。とくに，x₁＜x₂なるかぎりf(x₁)＜f(x₂)，またはf(x₁)＞f(x₂)となるとき，それぞれf(x)は狭義単調増加，または狭義単調減少であるといい，これらの場合を総称して狭義単調であるという。関数の単調性は，その定義域の一部の区間についていうこともある。…