Fundamental theorems of summability theory for double sequences via stretching by blocks

Autor:	Sami M. Hamid, Richard F. Patterson
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Double sequences Subsequences of a double sequences Pringsheim limit point P-convergent RH-regular Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-16 (2024)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-024-03226-x
Popis:	Abstract This paper extends fundamental theorems of summability theory to double sequences using stretching by blocks technique. We prove Steinhaus- and Buck-type theorems for double sequences, characterizing sequences that resist summability by RH-regular matrices and providing conditions for P-convergence. The preservation of P-divergence under block stretching is demonstrated, and a characterization of P-limit points via this method is established. We also show the impossibility of summing all block stretchings with a single RH-regular matrix. These results provide a more comprehensive framework for analyzing double sequences under matrix transformations.
Databáze:	Directory of Open Access Journals
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