Convergence Estimates of a Family of Approximation Operators

Abstract

The main object of this article is to consider a family of
approximation operators of exponential type, which has presumably
not been studied earlier due mainly to their seemingly complicated
behavior. We estimate and establish a quantitative asymptotic formula
in terms of the modulus of continuity with exponential growth,
a Korovkin-type result for exponential functions and also a
Voronovskaja-type asymptotic formula in the simultaneous approximation.