Generalized Absolute Riesz Summability of Orthogonal Series

  • K. KalaivaniEmail author
  • C. Monica
Conference paper
Part of the Trends in Mathematics book series (TM)


In this paper, for 1 ≤ k ≤ 2 and a sequence \(\gamma :=\{\gamma (n)\}_{n=1}^{\infty }\) that is quasi β-power monotone decreasing with \(\beta >1-\dfrac {1}{k},\) we prove the |A, γ|k summability of an orthogonal series, where A is Riesz matrix. For \(\beta >\frac {1}{2},\) we give a necessary and sufficient condition for |A, γ|k summability, where A is Riesz matrix. Our result generalizes the result of Moricz (Acta Sci Math 23:92–95, 1962) for absolute Riesz summability of an orthogonal series.


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Authors and Affiliations

  1. 1.Vellore Institute of TechnologyVelloreIndia

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