Abstract
In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series \((I_{w}^{\chi })_{w>0}.\) Further, we establish a representation formula and an inverse result of approximation for these operators. Finally, we give some examples of kernel functions to which the theory can be applied along with the graphical representation.
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Acknowledgements
The authors are extremely grateful to the reviewer for a careful reading of the manuscript and making valuable suggestions leading to a better presentation of the paper. The second author is thankful to the “Ministry of Human Resource and Development”, India for financial support to carry out his research work. The first author is supported by DST, SERB, India, Project file no: EEQ/2017/000201.
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Angamuthu, S.K., Bajpeyi, S. Direct and Inverse Results for Kantorovich Type Exponential Sampling Series. Results Math 75, 119 (2020). https://doi.org/10.1007/s00025-020-01241-0
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DOI: https://doi.org/10.1007/s00025-020-01241-0
Keywords
- Kantorovich type exponential sampling series
- pointwise convergence
- logarithmic modulus of continuity
- mellin transform
- inverse result.