Conditions for the pringsheim convergence of double sequences that are deferred cesàro summable
CitationSezer, S. A. (2021). Conditions for the pringsheim convergence of double sequences that are deferred cesàro summable. Fourth International Conference of Mathematical Sciences, Maltepe Üniversitesi. s. 1-3.
For a given real or complex valued double sequence (umn), its deferred Cesaro means are defined by ` D(11) mn (u) = 1 (βm − αm)(qn − pn) βm j=αm+1 qn k=pn+1 ujk (1) where (pn), (qn), (αm) and (βm) are the sequences of non-negative integers satisfying pn < qn, αm < βm and limn qn = ∞, limm βm = ∞. We say that (umn) is deferred Cesaro summable (briefly ( ` DC, 1, 1) summable) to if (1) tends to as m, n → ∞. Note that, if pn = 0, qn = n and αm = 0, βm = m, then corresponding (DC, 1, 1) method is the well known Cesaro summability ( ` C, 1, 1). In this extended abstract we give inverse conditions to obtain Pringsheim convergence of deferred Cesaro summable double ` sequences. We also give an inclusion relation with example.
SourceFourth International Conference of Mathematical Sciences
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