Absolute Summability Factors Related to the Summability Method |𝑵̅,𝒑𝒏, 𝜽|(𝝁)

Year 2019, , 1606 - 1611, 01.09.2019

Fadime Gökçe

https://doi.org/10.21597/jist.507772

Abstract

By (𝐴,𝐵), we denote the set of all sequences 𝜖 such that Σ𝑎𝑛𝜖𝑛 is summable 𝐵 whenever Σ𝑎𝑛 is summable 𝐴 where 𝐴 and 𝐵 are two summability methods. In this study, applying the main theorems in (Gökçe and Sarıgöl, 2018) to summability factors, we characterize the sets (|𝑁̅,𝑝𝑛,𝜃|(𝜇),|𝑁̅,𝑞𝑛|) and (|𝑁̅,𝑝𝑛,𝜃|(𝜇),|𝑁̅,𝑞𝑛,𝜓|(𝜆)). Also, in the special case, we get some well-known results.

Keywords

Absolute weighted summability, summability factors, matrix transformations, sequence spaces

|𝑵̅, 𝒑𝒏, 𝜽|(𝝁) Toplanabilme Metodu ile İlgili Mutlak Toplanabilme Çarpanları

Abstract

𝐴 ve 𝐵 iki toplanabilme metodu olmak üzere Σ𝑎𝑛, 𝐴 toplanabilir iken Σ𝑎𝑛𝜖𝑛, 𝐵 toplanabilir olacak şekildeki bütün 𝜖 dizilerinin kümesi (𝐴,𝐵) ile gösterilir ve 𝜖 dizisine toplanabilme çarpanı adı verilir. Bu çalışmada, (Gökçe ve Sarıgöl, 2018) tarafından verilen teoremler yardımıyla (|𝑁̅,𝑝𝑛,𝜃|(𝜇),|𝑁̅,𝑞𝑛|) ve (|𝑁̅,𝑝𝑛,𝜃|(𝜇),|𝑁̅,𝑞𝑛,𝜑|(𝜆)) toplanabilme çarpanları kümeleri karakterize edilmiştir. Ayrıca özel durumlarda, bilinen bazı sonuçlar elde edilmiştir.

Keywords

Mutlak ağırlıklı ortalama toplanabilme, toplanabilme çarpanı, matris dönüşümleri, dizi uzayları

References

• Gökçe F, Sarıgöl M A, 2018. A new series space |N ̅_P^θ |(μ) and matrix transformations with applications. Kuwait Journal of Science, 45(4): 1-8.
• Grosse-Erdmann KG, 1993. Matrix transformations between the sequence spaces of Maddox. Journal of Mathematical Analysis and Applications, 180(1): 223-238.
• Mitrinovic DS, 1970. Analytic Inequalties. Springer-Verlag, Berlin.
• Orhan C, Sarıgöl MA, 1993. On absolute weighted mean summability. The Rocky Mountain Journal of Mathematics, 23(3): 1091-1097.
• Sarıgöl MA, 2016. Norms and compactness of operators on absolute weighted mean summable series. Kuwait Journal of Science, 43(4): 68-74.
• Sarıgöl MA, 2013. An inequality for matrix operators and its applications. Journal of Classical Analysis, 2(2): 145-150.
• Sarıgöl MA, 2011. Matrix transformatins on fields of absolute weighted mean summability. Studia Scientiarum Mathematicarum Hungarica, 48(3): 331-341.
• Sarıgöl MA, Bor H, 1995. Characterization of absolute summability factors. Journal of Mathematical Analysis and Applications, 195 (2): 537-545.