Abstract

A non-empty set satisfying the properties of distance - identity of indiscernibles, symmetry, and stronger version of triangle inequality (called ultra metric property) is said to have Non-Archimedean or Ultrametric valuation. A sequence of elements of K is said to be statistically convergent to the number L, if for a given n, the set of all elements having distance to L greater than any arbitrary small real value divided by 'n' equals zero. In this present article, based on work by Aljimi etal [3], we obtain necessary and sufficient condition between Statistically Norlund Euler Convergence and statistically summable of a sequence in ultra-metric field. Further discussed conditions for the convergence of Norlund Euler Summable sequence of order r, worked by Aljimi et al.[3].

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