Abstract
The aim of this chapter is to present and study some recent development in summability theory and its applications. More recently, neutrosophic normed space (NNS) and the statistical convergence for ordinary (single) sequences in NNS has been studied. This chapter provides an overview on statistical convergence and statistical Cauchy for double sequences in NNS and specifically focuses on statistical completeness in connection with a NNS. We know that ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the ideal convergence of double sequences in NNS. That is, in this chapter, we study the concept of ideal convergence and ideal Cauchy for double sequences in NNS. The chapter also aims to analyze studies which criticize the concepts of I * 2-convergence, I * 2-Cauchy and I * 2-Cauchy for double sequences in NNS. The fundamental properties of these concepts with regard to NN N are investigated. The results of the chapter are expected to be a source for researchers in the areas of convergence methods for sequences and applications in NNS.
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