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Generalized Vector-Valued Paranormed Sequence Spaces Determined by a Sequence of Orlicz Functions

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Ukrainian Mathematical Journal Aims and scope

We introduce a class of generalized vector-valued paranormed sequence spaces \( X\left[E,A,{\varDelta}_{\upupsilon}^m,M,p\right] \) by using a sequence of Orlicz functions M = (Mk), a nonnegative infinite matrix A = [ank], a generalized difference operator \( {\varDelta}_{\upupsilon}^m \) and a bounded sequence of positive real numbers pk with inf k pk > 0. The properties related to this space are studied under certain conditions. Some inclusion relations are obtained and a result related to the subspace with Orlicz functions satisfying the Δ2-condition is also proved.

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Authors and Affiliations

  1. Dr. Harisingh Gour University, Sagar, India

    A. K. Verma & S. Kumar

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  1. A. K. Verma
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  2. S. Kumar
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Correspondence to S. Kumar.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 4, pp. 486–495, April, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i4.6549.

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Verma, A.K., Kumar, S. Generalized Vector-Valued Paranormed Sequence Spaces Determined by a Sequence of Orlicz Functions. Ukr Math J 74, 551–562 (2022). https://doi.org/10.1007/s11253-022-02082-6

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  • DOI: https://doi.org/10.1007/s11253-022-02082-6

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