Symmetrically continuous function

In mathematics, a function f: mathbb{R} to mathbb{R} is symmetrically continuous at a point x if

lim_{hto 0} f(x+h)-f(x-h) = 0.

The usual definition of continuity implies symmetric continuity, but the converse is not true.

See also


  • Thomson, Brian S. (1994). Symmetric Properties of Real Functions. Marcel Dekker. ISBN 0-8247-9230-0.

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