Necessary and Sufficient Tauberian Conditions for Logarithmic Summable Sequences in Two-Normed Spaces
Makaleler > Tam Makale · 2025
Yazarlar: Zerrin Önder, Sefa Anıl Sezer, İbrahim ÇANAK
Boletim da Sociedade Paranaense de Matemática, ESCI İndekslerine Giren Dergi, Uluslararası, Scopus, 2025, cilt 43, ss 1-11
DOI: 10.5269/bspm.64881
Özet
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 Móricz-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.