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Functions having more than one parameter can be strict or non-strict in each parameter independently, as well as jointly strict in several parameters simultaneously. As an example, the if-then-else expression of many programming languages, called ?: in languages inspired by C, may be thought of as a function of three parameters.
The function () = has ″ = >, so f is a convex function. It is also strongly convex (and hence strictly convex too), with strong convexity constant 2. The function () = has ″ =, so f is a convex function. It is strictly convex, even though the second derivative is not strictly positive at all points.
A strict programming language is a programming language that only allows strict functions (functions whose parameters must be evaluated completely before they may be called) to be defined by the user. A non-strict programming language allows the user to define non-strict functions, and hence may allow lazy evaluation.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .
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. [2] It is often attached to a technical term to indicate that the exclusive meaning of the term is to be understood.
The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
Strictly convex function, a function having the line between any two points above its graph; Strictly convex polygon, a polygon enclosing a strictly convex set of points; Strictly convex set, a set whose interior contains the line between any two points; Strictly convex space, a normed vector space for which the closed unit ball is a strictly ...
If the inequality is strict (a < b, a > b) and the function is strictly monotonic, then the inequality remains strict. If only one of these conditions is strict, then the resultant inequality is non-strict. In fact, the rules for additive and multiplicative inverses are both examples of applying a strictly monotonically decreasing function.