New Approach in Logarithmic Summability of Sequences

in Neutrosophic Normed Spaces

M. Jeyaraman^*, P. Jenifer, U. Praveena

Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India
Emails: jeya.math@gmail.com; jeni.deepan2013@gmail.com; upraveenasvg@gmail.com

Abstract

We introduce logarithmic summability in Neutrosophic Normed Spaces [NNS] and give some Taubarian conditions for which logarithmic summability yields convergence in NNS. Besides we define the concept of slow oscillation with respect to logarithmic summability in NNS, Investigate its relation with the concept of q-boundedness and give Taubarian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability.  A comparison theorem between CesaroSummability method and logarithmic summability method in NNS is also proved in the paper.

Keywords: Neutrosophic Normed Spaces; Logarithm Summability; Slow Oscillation; Taubarian Theorem.