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arXiv · 2604.19190

A Durrmeyer-type variant of Gr\"unwald Interpolation Operators

P. C. Vinaya
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Abstract

In this paper, we construct a Durrmeyer-type variant of Gr\"unwald interpolation operators on the space $L^p[0,{\pi}]$. 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.

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P. C. Vinaya. 2026-04-21. A Durrmeyer-type variant of Gr\"unwald Interpolation Operators. https://arxiv.org/abs/2604.19190

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