Abstract
In this article we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to \(L_{p}\) norm for \(
 1\leq p\leq \infty ,\) 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 produced in this article are almost sharp, containing neat 
 constants, and they reflect the high order of differentiability of involved
 function.
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