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 M\'{o}ricz-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.
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Funding data
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Türkiye Bilimsel ve Teknolojik Araştırma Kurumu
Grant numbers 118C577
