Approximation by Durrmeyer Type Exponential Sampling Operators

Abstract

In the present article, we derive some approximation results concerning the order of convergence for a family of Durrmeyer type exponential sampling operators. Further, we improve the rate of approximation by constructing linear combinations of these operators. At the end, we provide a few examples of the kernel functions to which the presented theory can be applied along with the graphical representation.

Keywords:

• Durrmeyer type exponential sampling operators
• Mellin derivative
• Mellin transform
• Peetre K-functional

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 41A35
• 30D10
• 94A20
• 41A25

Acknowledgments

The authors want to thank the reviewers for their careful reading and evaluation of the present paper. Ilaria Mantellini has been partially supported by the “Gruppo Nazionale per l’Analisi Matematica e Applicazioni (GNAMPA)” of the “Istituto di Alta Matematica (INDAM)” as well as by the projects “Ricerca di Base 2019 of University of Perugia (title: Misura, Integrazione, Approssimazione e loro Applicazioni)” and “Progetto Fondazione Cassa di Risparmio cod. nr. 2018.0419.021 (title: Metodi e Processi di Intelligenza artificiale per lo sviluppo di una banca di immagini mediche per fini diagnostici (B.I.M.))”.

Additional information

Funding

Shivam Bajpeyi is thankful to the” Ministry of Human Resource and Development”, India for financial support to carry out his research work. Sathish Kumar is supported by DST, SERB, India, Research Project file no: EEQ/2017/000201.