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Modular convergence in H-Orlicz spaces of Banach valued functions

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Abstract

In this article we develop the theory of H-Orlicz space generated by generalised Young function. Modular convergence of H-Orlicz space for the case of vector-valued functions and norm convergence in \(\mathcal {H}^\theta (X, \overline{\mu })\) where X is any Banach space are discussed. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed.

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Acknowledgements

The authors would like to thank the reviewer for reading the manuscript carefully and making valuable suggestions that significantly improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Assam Don Bosco University, Sonapur, Guwahati, Assam, 782402, India

    Hemanta Kalita

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, 781014, India

    Bipan Hazarika

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  1. Hemanta Kalita
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  2. Bipan Hazarika
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Kalita, H., Hazarika, B. Modular convergence in H-Orlicz spaces of Banach valued functions. Rend. Circ. Mat. Palermo, II. Ser 72, 3905–3916 (2023). https://doi.org/10.1007/s12215-023-00871-x

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