Dergiler / Konuralp Journal of Mathematics / 2025 / Volume: 13 Issue: 2

Entire Four-Dimensional Summation Methods

Fatih Nuray(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0003-0160-4001
Richard F. Patterson(University of North Florida)
Sayfa
—
Yayın Tarihi
2025-10-31
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Furthermore, we present a theorem addressing the consistency of these entire summation methods.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we establish the necessary and sufficient conditions for a four-dimensional matrix to map entire double-indexed sequences onto themselves, referring to such transformations as entire methods.
📊
Temel Bulgular & Veri:In this study, we establish the necessary and sufficient conditions for a four-dimensional matrix to map entire double-indexed sequences onto themselves, referring to such transformations as entire methods.
💡
Sonuç & Katkı:Furthermore, we present a theorem addressing the consistency of these entire summation methods.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Double sequence · P-limit · four-dimensional summability method

Abstract

In this study, we establish the necessary and sufficient conditions for a four-dimensional matrix to map entire double-indexed sequences onto themselves, referring to such transformations as entire methods. Furthermore, we present a theorem addressing the consistency of these entire summation methods.

🔖

Bu Makaleye Atıf Yap

Nuray, F., Patterson, R. F. (2025). Entire Four-Dimensional Summation Methods. Konuralp Journal of Mathematics, Volume: 13 Issue: 2. https://ajindex.com/articles/1521467

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Agnew, R. P., Inclusion Relations Among Methods of Summability Compounded form Given Matrix Methods, Aru. Mat. 2, (1952), 361–374.
  2. Aizenberg, L. A. and Yuzhakov, A. P., Integral representations and residues in multidimensional complex analysis, Translation of Mathematical Monographs, AMS, 58, (1983).
  3. Brown, H. I., Entire methods of summation, Compos. Math., 21 (1), (1969), 35–42.
  4. Hamilton, H. J., Transformations of Multiple Sequences, Duke Math. J., 2 (1936), 29 – 60.
  5. Hardy, H. G., Divergent Series, Oxford. (1949).
  6. Limaye, B. V. and Zeltser, M., On the Pringsheim convergence of double series, Proc. Est. Acad. Sci., 58 (2), (2009), 108—121.
  7. Nuray, F., Bounded index and four-dimensional summability methods. Novi Sad J. Math., 49 (2), (2019), 73–85.
  8. Bandura, A. and Nuray, F., Entire Bivariate Functions of Exponential Type II, Matematychni Studii, 59 (2), (2023), 156–167.
  9. Fricke, G. H., Roy, R. and Shah S. M., Bounded index, entire solutions of ordinary differential equations and summability methods, Int. J. of Math. and Math. Sci. 4 (3), (1981), 417–434.
  10. Patterson, R. F., A theorem on entire four-dimensional summability methods, Appl. Math. and Comput., 219, (2013), 7777–7782,
  11. Patterson, R. F., Four-dimensional matrix characterization of absolute summability, Soochow J. Math., 30 (1), (2004), 21–26.
  12. Patterson, R. F., Analogues of some Fundamental Theorems of Summability Theory, Int. J. Math. Math. Sci., 23 (1), (2000), 1–9.
  13. Pringsheim, A., Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann., 53 (1900), 289–32.
  14. Robison, G. M., Divergent Double Sequences and Series, Amer. Math. Soc. Trans., 28 (1926), 50–73.
  15. Zeltser, M., On conservative matrix methods for double sequence spaces, Acta Math. Hungar., 95 (3), (2002), 225–242.