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Order of Approximation for Exponential Sampling Type Neural Network Operators

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Abstract

In the present article, we derive certain direct approximation results for the family of exponential sampling type neural network operators. The Voronovskaja type theorem of convergence for these operators is proved. Further, the Jackson-type inequalities concerning the order of approximation for these family of operators are established by utilizing the notion of logarithmic modulus of continuity for the involved functions and their higher derivatives. In order to improve the order of convergence, we provide a constructive mechanism by considering the linear combination of these operators. At the end, we also discuss a few numerical examples based on the presented theory.

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Acknowledgements

The author is thankful to the anonymous reviewers for a careful reading and making valuable suggestions leading to a better presentation of the manuscript.

Funding

The author would like to acknowledge the financial support through project no. CRG/2019/002412 funded by the Department of Science and Technology, Government of India.

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  1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Shivam Bajpeyi

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Correspondence to Shivam Bajpeyi.

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Bajpeyi, S. Order of Approximation for Exponential Sampling Type Neural Network Operators. Results Math 78, 99 (2023). https://doi.org/10.1007/s00025-023-01879-6

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