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Estimates for the Neural Network Operators of the Max-Product Type with Continuous and p-Integrable Functions

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Abstract

In this paper we prove quantitative estimates for the Kantorovich version of the neural network operators of the max-product type, in case of continuous and p-integrable functions. In the first case, the estimate is expressed in terms of the modulus of continuity of the functions being approximated, while in the second case, we exploit the Peetre’s K-functionals.

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Acknowledgements

The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The authors are partially supported by the “Department of Mathematics and Computer Science” of the University of Perugia (Italy). Moreover, the first author of the paper holds a research grant (Post-Doc) funded by the INdAM, and finally, he has been partially supported within the 2017 GNAMPA-INdAM Project “Approssimazione con operatori discreti e problemi di minimo per funzionali del calcolo delle variazioni con applicazioni all’imaging”.

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  1. Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123, Perugia, Italy

    Danilo Costarelli & Gianluca Vinti

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  1. Danilo Costarelli
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  2. Gianluca Vinti
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Correspondence to Danilo Costarelli.

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Costarelli, D., Vinti, G. Estimates for the Neural Network Operators of the Max-Product Type with Continuous and p-Integrable Functions. Results Math 73, 12 (2018). https://doi.org/10.1007/s00025-018-0790-0

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  • DOI: https://doi.org/10.1007/s00025-018-0790-0

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