Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators

Serkan Ayan; Nurhayat İspir

doi:10.3934/mfc.2022056

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2023, Volume 6, Issue 3: 354-368. Doi: 10.3934/mfc.2022056

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Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators

Serkan Ayan^1, , and
Nurhayat İspir^1,2,

1.
Bursa Technical University Faculty of Engineering and Natural Science, Department of Mathematics, Bursa, 16310, Turkey
2.
Gazi University Faculty of Science, Department of Mathematics, Ankara, 06500, Turkey

^*Corresponding author: Serkan Ayan
^*Corresponding author: Serkan Ayan

Dedicated to Prof. Vijay Gupta on the occasion of his 60th birthday.

Received: July 2022

Revised: November 2022

Early access: December 2022

Published: August 2023

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Abstract

In this study, we prove the convergence theorems on the space of compactly supported functions and in the general setting of Orlicz spaces for a general class of Kantorovich type discrete operators defined by Carlo Bardaro and Ilaria Mantellini. We also define the generalized Boolean sum (GBS) operator for the class of bivariate Kantorovich type discrete operators and examine the approximation properties of GBS operators in the space of Bögel functions.

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Mathematics Subject Classification: 41A35, 41A30, 41A10, 94A12.

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References

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