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<p>The prime objective of this paper is to define new difference double sequence spaces in the domain of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal {L}_p\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mathcal {L}_\infty\)</EquationSource> </InlineEquation> via the double difference operator <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(_2\Delta ^{\gamma , \mu }\)</EquationSource> </InlineEquation> of orders <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\gamma , \mu\)</EquationSource> </InlineEquation>. The above spaces are normed linear spaces and they are linearly isomorphic to the spaces <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\({\mathcal {L}_p}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\({\mathcal {L}_\infty }\)</EquationSource> </InlineEquation> for <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(1\le p&lt;\infty\)</EquationSource> </InlineEquation>. Also, some inclusion relations among them are derived.</p>

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New classes of double sequences in the domain of \({\mathcal {L}_p}\) and \({\mathcal {L}_\infty }\)

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • S. Samantaray,
  • L. Nayak,
  • P. Baliarsingh

摘要

The prime objective of this paper is to define new difference double sequence spaces in the domain of \(\mathcal {L}_p\) and \(\mathcal {L}_\infty\) via the double difference operator \(_2\Delta ^{\gamma , \mu }\) of orders \(\gamma , \mu\) . The above spaces are normed linear spaces and they are linearly isomorphic to the spaces \({\mathcal {L}_p}\) and \({\mathcal {L}_\infty }\) for \(1\le p<\infty\) . Also, some inclusion relations among them are derived.