Asymmetric fractal approximation of functions in the space $L_p^{\alpha ,\beta }(I)$

Abstract

Sufficient conditions to the sequence of
functions that are the result of fractal iterated operator
transformation into some function coincided on the segment.
We obtained
error estimates for fractal approximation, which is analogous to Barnsley theorem
about a collage of fractal approximation in the space of integrable
in $ p $ degree functions with asymmetric metric. Super fractal
approximation ofsets has been adapted to approximation of functions on $L_p^{\alpha,\beta}(I)$.