Lipschitz condition

English

Etymology

Named after Rudolf Lipschitz (1832–1903), a German mathematician. It is called a "condition" because it is a sufficient (but not necessary) condition for continuity of a function.

Noun

Lipschitz condition (plural Lipschitz conditions)

1. (mathematical analysis) A property which can be said to be held by some point in the domain of a real-valued function if there exists a neighborhood of that point and a certain constant such that for any other point in that neighborhood, the absolute value of the difference of their function values is less than the product of the constant and the absolute value of the difference between the two points.

References

• Tom M. Apostol (1957), Mathematical Analysis : A Modern Approach to Advanced Calculus, Reading, Massachusetts, U.S.A.: Addison-Wesley Publishing Company, Inc., published 1960, LCCN 57008707, §5-2, page 87