**Inverse function theorem** — In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… … Wikipedia

**Open mapping theorem (functional analysis)** — In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is… … Wikipedia

**Inverse function** — In mathematics, if fnof; is a function from A to B then an inverse function for fnof; is a function in the opposite direction, from B to A , with the property that a round trip (a composition) from A to B to A (or from B to A to B ) returns each… … Wikipedia

**Inverse problem** — An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth s gravity field, then we might … Wikipedia

**Banach fixed-point theorem** — In mathematics, the Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of… … Wikipedia

**Implicit function theorem** — In the branch of mathematics called multivariable calculus, the implicit function theorem is a tool which allows relations to be converted to functions. It does this by representing the relation as the graph of a function. There may not be a… … Wikipedia

**Quasiconformal mapping** — In mathematics, the concept of quasiconformal mapping, introduced as a technical tool in complex analysis, has blossomed into an independent subject with various applications. Informally, a conformal homeomorphism is a homeomorphism between plane … Wikipedia

**Contraction mapping** — In mathematics, a contraction mapping, or contraction, on a metric space (M,d) is a function f from M to itself, with the property that there is some nonnegative real number k < 1 such that for all x and y in M, The smallest such value of k is … Wikipedia

**Banach fixed point theorem** — The Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps… … Wikipedia

**Closed graph theorem** — In mathematics, the closed graph theorem is a basic result in functional analysis which characterizes continuous linear operators between Banach spaces in terms of the operator graph. Contents 1 The closed graph theorem 2 Generalization 3 See… … Wikipedia