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<p>In this paper, we introduce and study the concept of lacunary weighted mean convergence for sequences in real or complex normed spaces. We establish its relation with classical lacunary convergence by proving inclusion relations and presenting counterexamples to show their strictness. Moreover, we demonstrate that under suitable regularity conditions on the weight sequence, both notions of convergence coincide.</p>

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Lacunary Weighted Mean Convergence of Sequences

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Pranab Jyoti Dowari,
  • Binod Chandra Tripathy

摘要

In this paper, we introduce and study the concept of lacunary weighted mean convergence for sequences in real or complex normed spaces. We establish its relation with classical lacunary convergence by proving inclusion relations and presenting counterexamples to show their strictness. Moreover, we demonstrate that under suitable regularity conditions on the weight sequence, both notions of convergence coincide.