Zipper Fractal Functions with Variable Scalings

Zipper fractal interpolation function (ZFIF) is a generalization of through an
 improved version iterated system by using binary parameter called signature. The signature
 allows the horizontal scalings to be negative. ZFIFs have complex geometric structure, and they can
 non-differentiable on dense subset an interval I. In this paper, we construct k-times continuously
 differentiable with variable scaling functions Some properties like positivity, monotonicity,
 convexity zipper one-sided approximation for continuous a
 are studied. existence Schauder basis space
 continuously space p-integrable p ? [1,?) are
 We introduce versions full Müntz theorem p-integrable
 I [1,?).