Summary: Symmetric and quantum symmetric derivatives of Lipschitz
functions
J. Marshall Ash
Abstract. The symmetric derivative of a real valued function f at the real
number x is de...ned to be
lim
h&0
f (x + h) f (x h)
2h
when that limit exists, and if additionally x 6= 0; the quantum symmetric
derivative is de...ned to be
lim
q&1
f (qx) f q 1x
qx q 1x
when that limit exists. An increasing function ' : R+ ! R satisfying
lim
h&0
' (h) =h1=2
= 0

Source: Ash, J. Marshall - Department of Mathematical Sciences, DePaul University

Collections: Mathematics