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Convergence in \(\varphi \)-variation for Mellin-type nonlinear integral operators

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Abstract

In the present paper, we examine Mellin-type nonlinear integral operators equipped with the Haar measure. Using \(\varphi \)-absolutely continuous functions, we obtain some approximations via summability process. Order of convergence is also observed. In addition, we have a general characterization theorem for \(\varphi \)-absolutely continuous functions. Finally, we give an application of our study with some illustrations and numerical computations.

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Acknowledgements

This study is supported by the Scientific and Technological Research Council of Turkey, Grant No: 119F262.

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  1. Department of Mathematics, Hacettepe University, 06800, Çankaya, Ankara, Turkey

    İsmail Aslan

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  1. İsmail Aslan
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Correspondence to İsmail Aslan.

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Communicated by S Ponnusamy.

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Aslan, İ. Convergence in \(\varphi \)-variation for Mellin-type nonlinear integral operators. J Anal (2024). https://doi.org/10.1007/s41478-024-00760-1

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