SavedAdd your journal

Journals / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2019 / Cilt: 9 - Sayı: 1

TAUBERIAN THEOREMS FOR THE PRODUCT OF BOREL AND LOGARITHMIC METHODS OF SUMMABILITY

Sefa Anıl SEZER
Pages
165–171
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also obtain some classical Tauberian theorems and their generalizations as special cases of our main theorems.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we show that if a sequence is summable by the product method (B)(`, k), then it is also summable by the logarithmic method (`, k), provided two-sided conditions of Hardy-type are satisfied.
📊
Key Findings & Data:In this paper, we show that if a sequence is summable by the product method (B)(`, k), then it is also summable by the logarithmic method (`, k), provided two-sided conditions of Hardy-type are satisfied.
💡
Conclusion & Impact:We also obtain some classical Tauberian theorems and their generalizations as special cases of our main theorems.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

In this paper, we show that if a sequence is summable by the product method (B)(`, k), then it is also summable by the logarithmic method (`, k), provided two-sided conditions of Hardy-type are satisfied. We also obtain some classical Tauberian theorems and their generalizations as special cases of our main theorems.

🔖

Cite This Article

SEZER, S. A. (2019). TAUBERIAN THEOREMS FOR THE PRODUCT OF BOREL AND LOGARITHMIC METHODS OF SUMMABILITY. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 1, 165–171. https://ajindex.com/articles/341273

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  1. Borwein, D., (1958), A logarithmic method of summability, J. Lond. Math. Soc., 33, pp. 212–220
  2. Braha, N. L., (2016), A Tauberian theorem for the generalized N¨orlund-Euler summability method, J. Inequal. Spec. Funct., 7 (4), pp. 137–142
  3. C¸ anak ˙I., (2014), Some extended Tauberian theorems for (A) (k) (C, α) summability method, Acta Sci., Technol., 36 (4), pp. 679–683
  4. C¸ anak, ˙I., Erdem, Y. and Totur, (2010), U., Some Tauberian theorems for ( ¨ A)(C, α) summability method, Math. Comput. Modelling, 52 (5-6), pp. 738–743
  5. Erdem, Y. and C¸ anak, ˙I., (2016), A Tauberian theorem for the product of Abel and Ces`aro summability methods, Georgian Math. J., 23 (3), pp. 343–350
  6. Erdem, Y., C¸ anak, ˙I. and Allahverdiev, B., (2015), Two theorems on the product of Abel and Ces`aro summability methods, C. R. Acad. Bulg. Sci., 68 (3), pp. 287–294
  7. Hardy, G. H., (1949), Divergent Series, Clarendon Press, Oxford
  8. Ishiguro, K., (1963), Tauberian theorems concerning the summability methods of logarithmic type, Proc. Japan Acad., 39, pp. 156–159
  9. Kwee, B., (1967), A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc., 63 (2), pp. 401–405
  10. Kwee, B., (1968), Some Tauberian theorems for the logarithmic method of summability, Canad. J. Math., 20, pp. 1324–1331
  11. Kwee, B., (1989), The relation between the Borel and Riesz methods of summation, Bull. London Math. Soc., 21 (4), pp. 387–393
  12. Loku, V. and Braha, N. L., (2017), Tauberian theorems by weighted summability method, Armen. J. Math., 9 (1), pp. 35–42
  13. Mure¸san, M., (2008), A Concrete Approach to Classical Analysis, Springer, Berlin
  14. M´oricz, F., (2004), Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences, Analysis (Munich), 24 (2), pp. 127–145
  15. Parameswaran, M. R., (1957), Some product theorems in summability, Math. Z., 68, pp. 19–26
  16. Parameswaran, M. R., (1994), New Tauberian theorems from old, Canad. J. Math., 46 (2), pp. 380– 394
  17. Ramanujan, M. S., (1958), On products of summability methods, Math. Z., 69, pp. 423–428
  18. Sezer, S. A. and C¸ anak, ˙I., (2018), Tauberian theorems for the summability methods of logarithmic type, Bull. Malays. Math. Sci. Soc., 41 (4), pp. 1977–1994
  19. Sz´asz, O., (1952), On products of summability methods, Proc. Amer. Math. Soc., 3, pp. 257–263
  20. Totur, U. and Okur, M. A., (2016), On logarithmic av