Fixed points (mathematics) | Mathematical analysis | Topology

Coincidence point

In mathematics, a coincidence point (or simply coincidence) of two functions is a point in their common domain having the same image. Formally, given two functions we say that a point x in X is a coincidence point of f and g if f(x) = g(x). Coincidence theory (the study of coincidence points) is, in most settings, a generalization of fixed point theory, the study of points x with f(x) = x. Fixed point theory is the special case obtained from the above by letting X = Y and taking g to be the identity function. Just as fixed point theory has its fixed-point theorems, there are theorems that guarantee the existence of coincidence points for pairs of functions. Notable among them, in the setting of manifolds, is the Lefschetz coincidence theorem, which is typically known only in its special case formulation for fixed points. Coincidence points, like fixed points, are today studied using many tools from mathematical analysis and topology. An equaliser is a generalization of the coincidence set. (Wikipedia).

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From playlist Determining Odd and Even Functions

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Here, I show an example which shows how to find the distance between two points. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Random Math Videos

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From playlist Introduction to Decimals

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From playlist Using the Distance Formula / Midpoint Formula

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From playlist Introduction to Vectors

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From playlist Calculus / Third Semester / Multivariable Calculus

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From playlist Euclid

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Related pages

Manifold | Domain of a function | Lefschetz fixed-point theorem | Identity function | Mathematics | Function (mathematics) | Fixed point (mathematics) | Topology | Equaliser (mathematics) | Theorem | Mathematical analysis | Special case