Approximation of functions in a certain Banach space by some generalized singular integrals

Abstract

We introduced the $ q $-Picard, the $ q $-Picard-Cauchy, the $ q $-Gauss-Weierstrass, and the $ q $-truncated Picard singular integrals. Using the last three mentioned integrals, the orders of approximation for functions from a generalized Hölder space were determined, both in the $ L^{p} $-norm and in the generalized Hölder-norm.

Keywords

• degree of approximation
• $ q $-singular integrals
• modulus of continuity
• generalized hölder class
• generalized minkowski inequality