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25 relations: Brouwer fixed-point theorem, Caristi fixed-point theorem, Cauchy sequence, Compact space, Complete metric space, Contraction mapping, Fichera's existence principle, Fixed point (mathematics), Fixed-point theorem, Fixed-point theorems in infinite-dimensional spaces, Infinite compositions of analytic functions, Inverse function theorem, Iterated function, James Dugundji, Lipschitz continuity, Mathematical induction, Metric space, Open content, Ordinary differential equation, Picard–Lindelöf theorem, Rate of convergence, Set (mathematics), Stefan Banach, T1 space, Ultrametric space.
Brouwer fixed-point theorem
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer.
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Caristi fixed-point theorem
In mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself.
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Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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Contraction mapping
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M,d) is a function f from M to itself, with the property that there is some nonnegative real number 0\leq k such that for all x and y in M, The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps.
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Fichera's existence principle
In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954.
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Fixed-point theorem
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x).
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Fixed-point theorems in infinite-dimensional spaces
In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem.
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Infinite compositions of analytic functions
In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence/divergence of these expansions.
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Inverse function theorem
In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point.
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Iterated function
In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.
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James Dugundji
James Dugundji (August 30, 1919 – January, 1985) was an American mathematician, a professor of mathematics at the University of Southern California.
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Lipschitz continuity
In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Open content
Open content is a neologism coined by David Wiley in 1998 which describes a creative work that others can copy or modify freely, without asking for permission.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Picard–Lindelöf theorem
In mathematics, in the study of differential equations, the Picard–Lindelöf theorem, Picard's existence theorem or Cauchy–Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.
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Rate of convergence
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Stefan Banach
Stefan Banach (30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians.
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T1 space
In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other.
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Ultrametric space
In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\.
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References
[1] https://en.wikipedia.org/wiki/Banach_fixed-point_theorem
