vähenemisfunktsiooni

A vähenemisfunktsioon, in mathematics, is a function where for any two values x1 and x2 in the domain of the function, if x1 is less than x2, then the function's value at x1 is greater than or equal to the function's value at x2. This can be expressed formally as: if x1 < x2, then f(x1) >= f(x2).

This property signifies a non-increasing trend in the function's output as the input increases. It is important to distinguish a vähenemisfunktsioon from a strictly decreasing function. A strictly decreasing function requires that if x1 < x2, then f(x1) > f(x2), meaning the function's value must always decrease, never stay the same.

Vähenemisfunktsioonid appear in various areas of mathematics and computer science. For example, in calculus, the derivative of a vähenemisfunktsioon is less than or equal to zero over its domain. In algorithm analysis, particularly in the context of optimization algorithms, understanding whether a cost function is vähenemisfunktsioon can be crucial for determining convergence properties. Similarly, in probability theory, cumulative distribution functions are typically non-decreasing, while survival functions are non-increasing, which is a form of vähenemisfunktsioon. The concept is fundamental for analyzing trends and monotonic behavior in mathematical models.