Global Smoothness Preservation and Simultaneous Approximation by Generalized Discrete Singular Operators


In this chapter we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to Lp-norm for 1 ≤ p ≤ ∞, by involving higher order moduli of smoothness. Additionally, we study their simultaneous approximation to the unit operator with rates involving the modulus of smoothness. The Jackson type inequalities that produced in this chapter are almost sharp, containing neat constants, and they reflect the high order of differentiability of involved function. It follows [4].

Publication Title

Series on Concrete and Applicable Mathematics