Category

Types of functions

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continuous function

function such that the preimage of an open set is open

periodic function

function that repeats its values in regular intervals or periods

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.

mathematical function that preserves distinctness

surjective function

function such that every element of the codomain has a preimage

even and odd functions

types of mathematical functions

monotonic function

function between ordered sets that preserves or reverses the given order

identity function

function that always returns the same value that was used as its argument

convex function

real function with secant line between points above the graph itself

elementary function

mathematical function built from basic functions and elementary operations

indicator function

function that returns 1 if an element is present in a specified subset and 0 if absent; naturally isomorphic with a set's subsets

algebraic function

function that can be defined as the root of a polynomial equation

mapping from a mathematical space to the real or complex numbers

transfer function

mathematical function specifying the output of a component in an electronic or control system for each possible input

transcendental function

analytic function that does not satisfy a polynomial equation

Weierstrass function

function that is continuous everywhere but differentiable nowhere

concave function

negative of a convex function

homogeneous function

function with multiplicative scaling behaviour

vector-valued function

function valued in a vector space; typically a real or complex one

bounded function

function or sequence whose possible values form a bounded set

real-valued function

function whose range is a subset of the real numbers

measurable function

function between measurable spaces

weight function

construct related to weighted sums and averages

window function

function used in signal processing

piecewise linear function

real-valued function composed of straight line segments

orthogonal functions

type of function

simple function

complex function on a measurable space that is piecewise constant with a finite number of measurable regions

element of a basis for a function space

almost periodic function

function that "converges" to periodicity

In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function's values at each element. There are numerous examples of subadditive functions in various areas of mathematics, particularly norms and square roots. Additive maps are special cases of subadditive functions.

locally integrable function

function which is integrable on every compact subset of its domain of definition

subharmonic function

function f such that, if f≤h on the boundary of a ball for any harmonic function h, then f≤h also inside the ball

singular function

continuous monotonic nonconstant function with zero derivative almost everywhere

quasiconvex function

function for which every set of inputs whose value is below a given threshold is convex

negligible function

mathematical function

Hermitian function

complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign

positive-definite function

bimodal function

functions obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions

sublinear function

Type of function in linear algebra

Antiholomorphic function

Function family in complex analysis

binary function

function that takes two inputs

Z-module homomorphism

quasiperiodic function

mathematical function

Mathematical map

superadditivity

In mathematics, a function f is superadditive if f(x+y) \geq f(x) + f(y) for all x and y in the domain of f.

Hardy–Littlewood maximal function

Mathematical operator in real and harmonic analysis

list of periodic functions

Wikimedia list article

barrier function

continuous function whose value increases to infinity

Support function

Support function

coercive function

mathematical function that "grows rapidly" at the extremes of the space on which it is defined

Symmetrically continuous function

function defined on the set of conjugacy classes of a group

function between varieties that is given locally by polynomials

cardinal function

function that returns cardinal numbers

Closed convex function

constructible function

function whose values can be computed in a number of steps or a number of Turing-machine cells of order given by the function itself

slowly varying function

function in mathematics

proper convex function

concept in convex analysis

function that takes one argument. In computer science, a unary operator is a subset of unary function