Generalized vector-valued paranormed sequence spaces defined by a sequence of Orlicz functions

  • A. K. Verma Dr. Harisingh Gour Univ., Sagar, India
  • S. Kumar Dr. Harisingh Gour Univ., Sagar, India
Keywords: Orlicz function, Paranormed space, Difference sequence space, Normal space

Abstract

UDC 517.9

We introduced a class of generalized vector-valued paranormed sequence space $X[E,A,\Delta_v^m,M,p]$ by using a sequence of Orlicz functions $M=(M_k),$ a non-negative infinite matrix $A=[a_{nk}],$ generalized difference operator $\Delta_v^m$ and bounded sequence of positive real numbers $p_k$ with $\inf_k p_k>0.$ Properties related to this space are studied under certain conditions. Some inclusion relations are obtained and a result related to subspace with Orlicz functions satisfying $\Delta_2$-condition has also been proved.

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Published
20.05.2022
How to Cite
Verma, A. K., and S. Kumar. “Generalized Vector-Valued Paranormed Sequence Spaces Defined by a Sequence of Orlicz Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 4, May 2022, pp. 486 -95, doi:10.37863/umzh.v74i4.6549.
Section
Research articles