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On the classes of functions of generalized bounded variation

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Abstract

The properties of the class of functions of generalized bounded variation are studied. The “anomaly” feature of this class is revealed. There is the notation of absolute continuity with respect to \(((p_n), \phi )\) and it’s connection with the ordinary absolute continuity is investigated. The problems of approximation by Steklov’s functions and singular integrals are studied.

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Acknowledgements

The authors are very grateful to the referees for the careful reading of the paper and helpful comments and remarks. Research supported by Shota Rustaveli National Science Foundation Grant FR-18-1599

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Correspondence to Teimuraz Akhobadze or Koba Ivanadze.

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Communicated by Sergey Astashkin.

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Akhobadze, T., Ivanadze, K. On the classes of functions of generalized bounded variation. Banach J. Math. Anal. 14, 762–783 (2020). https://doi.org/10.1007/s43037-019-00038-w

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  • DOI: https://doi.org/10.1007/s43037-019-00038-w

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