Weighted Approximation of Functions with Singularity by q-Baskakov Operators

By the weighted q-Baskakov operators, we approximate the class of functions with singularity in the point zero of the approximation order in this paper. Firstly, we defined the functions with singularities q-Baskakov operators in the Soblev space by point wise approximation and simultaneous approximation, while redefine modulus of smoothness and K-functional, get some information on q-Baskakov operators in (0, + ∞) on the nature of the singularity functions. While taking advantage of re-definition of the second order modulus of smoothness and some important inequalities has been such a positive approach converse.