Symmetrically continuous function

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

$\lim _{h\to 0}f(x+h)-f(x-h)=0.$

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

See also

• Symmetric derivative

References

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