  We derive a number of equivalent criterions for the variable exponent Hardy
type inequality |\frac{1}{x}\int_{0}^{x}f(t)dt|_{L^{p(.)}(0,1)}\leq
C|f|_{L^{p(.)}(0,1)}; f\geq 0. to hold, whenever the exponent $p:(0,1)\to
(1,\infty)$ is increasing or decreasing near small neighborhood of the origin.
