Approximation of Function in the Generalized Holder Metric

Jackson polynomial is an important interpolation polynomial in approximation fields, there are some results of interpolation and approximation about Jackson polynomials have been established, those results contained different metric or different methods, one of them is a result about interpolation and approximation of Jackson polynomials in holder metric, then holder metric was generalized in a sense, those theory about the generalized holder metric provide a new field for us, here two theorem about Jackson polynomial in generalized holder metric were established, and under generalized holder metric, Jackson polynomial and it's approximating function and conjugate function have special property.