A computational analysis of a family of Szász type operators based on Tricomi functions

This paper introduces a novel family of integral operators incorporating Tricomi functions. We derive explicit estimates for test functions and central moments, alongside establishing uniform convergence via the Korovkin theorem and approximation order through the first-order modulus of smoothness. Pointwise approximation results are further analyzed using Peetre’s K-functional, the second-order modulus of smoothness, and Lipschitz-type spaces. Finally, these theoretical developments are substantiated through comprehensive numerical experiments and graphical illustrations across varied parameter configurations.