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Two valued measure and summability of double sequences

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Abstract

In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO2) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO2).

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, West Bengal, India

    Pratulananda Das

  2. Department of Mathematics, F.C.College, Diamond Harbour, South 24 Prgs., Pin, 743331, West Bengal, India

    Santanu Bhunia

Authors
  1. Pratulananda Das
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  2. Santanu Bhunia
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Correspondence to Pratulananda Das.

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Das, P., Bhunia, S. Two valued measure and summability of double sequences. Czech Math J 59, 1141–1155 (2009). https://doi.org/10.1007/s10587-009-0081-8

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  • DOI: https://doi.org/10.1007/s10587-009-0081-8

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