Two valued measure and summability of double sequences
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In this paper, following the methods of Connor , we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely ) 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 . 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).
Keywordsdouble sequences μ-statistical convergence divergence and Cauchy criteria convergence divergence and Cauchy criteria in μ-density condition (APO2)
MSC 200040A30 40A05