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<p>We introduce a considerable convergence structure called <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {I}_{(\lambda )}-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">I</mi> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>statistical convergence of order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> with respect to seminorm <i>q</i>. In this paper, to further extend the notion of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>-statistical convergence, which is defined by Mursaleen (Math Slovaca 50:111–115, <CitationRef CitationID="CR13">2000</CitationRef>). We mainly focus on improving and generalizing some existing results on sequence spaces. Moreover, some detailed inclusion relations are established between these sequence spaces. We also leave a fruitful open problem.</p>

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GENERALIZED IDEAL STATISTICAL CONVERGENCE OF ORDER \(\theta \) WITH RESPECT TO SEMINORM q

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Ekrem Savaş

摘要

We introduce a considerable convergence structure called \(\mathcal {I}_{(\lambda )}-\) I ( λ ) - statistical convergence of order \(\theta \) θ with respect to seminorm q. In this paper, to further extend the notion of \(\lambda \) λ -statistical convergence, which is defined by Mursaleen (Math Slovaca 50:111–115, 2000). We mainly focus on improving and generalizing some existing results on sequence spaces. Moreover, some detailed inclusion relations are established between these sequence spaces. We also leave a fruitful open problem.