A Durrmeyer-type variant of Grünwald Interpolation Operators

Abstract

In this paper, we construct a Durrmeyer-type variant of Grünwald interpolation operators on the space $L^p[0,\ddot{I}€]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the convergence results using a Korovkin-type theorem in the setting of Banach function spaces. Furthermore, we obtain quantitative estimates for the convergence by means of the modulus of continuity and an appropriate $K$-functional.