Geodesic
Conditions under which convergence of a sequence or its certain subsequences follows from deferred Cesàro summability
Filomat, Tome 36 (2022) no. 3, p. 921

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DOI

Let (uᵤ : n = 1, 2, ...) be a sequence of real or complex numbers. We aim in this paper to determine necessary and/or sufficient conditions under which convergence of a sequence (uᵤ) or its certain subsequences follows from summability by deferred Cesàro means. We also investigate the limiting behavior of deferred moving averages of (uᵤ). The conditions in our theorems are one-sided if (uᵤ) is a sequence of real numbers, and two-sided if (uᵤ) is a sequence of complex numbers. The theory developed in this paper should be useful for developing more interesting and useful results in connection with other sophisticated summability means as well as to extend to other spaces like ordered linear spaces
DOI : 10.2298/FIL2203921S
Classification : 40E05, 40A05, 40G99
Keywords: Deferred Cesàro means, Tauberian conditions and theorems, moving averages, deferred slow decrease, deferred slow oscillation, ordered linear spaces 
Sefa Anıl Sezer; Ibrahim Çanak; Hemen Dutta. Conditions under which convergence of a sequence or its certain subsequences follows from deferred Cesàro summability. Filomat, Tome 36 (2022) no. 3, p. 921 . doi: 10.2298/FIL2203921S
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     title = {Conditions under which convergence of a sequence or its certain subsequences follows from deferred {Ces\`aro} summability},
     journal = {Filomat},
     pages = {921 },
     year = {2022},
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     number = {3},
     doi = {10.2298/FIL2203921S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203921S/}
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