• Necessary and sufficient conditions for inclusion relations for absolute summability

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/03/0243-0250

    • Keywords

       

      Absolute summability; weighted mean matrix; Cesáro matrix

    • Abstract

       

      We obtain a set of necessary and sufficient conditions for$$\left| {\bar N, p_n } \right|_k $$ to imply$$\left| {\bar N, q_n } \right|_s $$ for 1 <k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of$$\left| {\bar N, p_n } \right|_k $$ and$$\left| {\bar N, q_n } \right|_s $$.

    • Author Affiliations

       

      B E Rhoades1 Ekrem Savaş1 2

      1. Department of Mathematics, Indiana University, Bloomington, IN - 47405-7106, USA
      2. Department of Mathematics, Yüzüncü Yil University, Van, Turkey
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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