Necessary and Sufficient Tauberian Conditions for Logarithmic Summable Sequences in Two-Normed Spaces

Abstract

Our aim in this paper is to make a novel interpretation of the relation between the logarithmic summability method and convergence under the coverage of 2-normed spaces. In line with this aim, we introduce a necessary and sufficient Tauberian condition of Moricz-type for logarithmic summable sequences in these kinds of spaces. Following this, we investigate whether conditions designed as O-type such as the slow oscillation and Hardy-type conditions with respect to summability (& ell;, 1) due to the non-existence of relation of "order" in 2-normed spaces are the conditions needed for logarithmic summable sequences to be convergent.