SavedAdd your journal

Journals / Fundamental Journal of Mathematics and Applications / 2025 / Volume: 8 Issue: 4

Cesro Summable and Statistically Convergent Sequences in Polya's Sense

Elif Nuray Yıldırım(İSTANBUL TİCARET ÜNİVERSİTESİ)0000-0002-2934-892X
Fatih Nuray(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0003-0160-4001
Pages
—
Publication Date
2025-12-30
🏛️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)

Additionally, we examine the connection between strongly Polya summable and Polya statistically convergent sequences, particularly for bounded and unbounded cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper introduces and explores the concepts of Polya summability, strongly Polya summability, and statistical convergence in the Polya sense, establishing their relationships with classical summability methods, particularly Cesaro summability.
📊
Key Findings & Data:We provide sufficient conditions for their equivalence, highlight key distinctions, and demonstrate these results through explicit examples.
💡
Conclusion & Impact:Additionally, we examine the connection between strongly Polya summable and Polya statistically convergent sequences, particularly for bounded and unbounded cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Statistical convergence · Polya means · Polya statistically convergence

Abstract

This paper introduces and explores the concepts of Polya summability, strongly Polya summability, and statistical convergence in the Polya sense, establishing their relationships with classical summability methods, particularly Cesaro summability. We provide sufficient conditions for their equivalence, highlight key distinctions, and demonstrate these results through explicit examples. Notably, while every Cesaro summable sequence is Polya summable, the converse does not always hold. Additionally, we examine the connection between strongly Polya summable and Polya statistically convergent sequences, particularly for bounded and unbounded cases.

🔖

Cite This Article

Yıldırım, E. N., Nuray, F. (2025). Cesro Summable and Statistically Convergent Sequences in Polya's Sense. Fundamental Journal of Mathematics and Applications, Volume: 8 Issue: 4. https://doi.org/10.33401/fujma.1649410

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. G. Polya, Untersuchungen über Lücken und Singularitaten von Potenzreihen, Math. Zeit., 29(1929), 549–640. $ \href{/https://doi.org/10.1007/BF01180553}{\mbox{[CrossRef]}} $
  2. N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloq. Publ. 26, New York, 1940. $ \href{https://ia800801.us.archive.org/30/items/in.ernet.dli.2015.212279/2015.212279.Gap-And.pdf}{\mbox{[Web]}} $
  3. P. Leonetti, Thinnable ideals and invariance of cluster points, Rocky Mountain J. Math., 48(6) (2018), 1951–1961. $ \href{https://doi.org/10.1216/RMJ-2018-48-6-1951}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85057136196?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000450989900013}{\mbox{[Web of ScienceossRef]}} $
  4. M. Marinacci, An Axiomatic Approach to Complete Patience and Time Invariance, J. Econom. Theory, 83(1) (1998), 105–144. $ \href{https://doi.org/10.1006/jeth.1997.2451}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/0040635278?origin=resultslist}{\mbox{[Scopus]}} $
  5. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1951), 73-74.
  6. H. Fast, Sur la convergence statistique, Colloq. Math.,2(1951), 241-244. $ \href{http://matwbn.icm.edu.pl/ksiazki/cm/cm2/cm2137.pdf }{\mbox{[Web]}} $
  7. J.S. Connor, The statistical and strong p-Ces`aro convergence of sequences, Analysis, 8(1988), 47-63. $ \href{https://doi.org/10.1007/s43036-023-00272-y}{\mbox{[CrossRef]}} \href{https://www.scopus.com/pages/publications/85160247426?origin=resultslist}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000995348300001}{\mbox{[Web of ScienceossRef]}} $
  8. J.S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(1989), 194-198. $ \href{https://doi.org/10.4153/CMB-1989-029-3}{\mbox{[CrossRef]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:A1989AL52200010}{\mbox{[Web of ScienceossRef]}} $
  9. J.A. Fridy, On statistical convergence, Analysis,5(1985), 301-313. $ \href{https://www.scopus.com/pages/publications/0000363911?origin=resultslist}{\mbox{[Scopus]}} $
  10. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca,30(1980), 139-150. $ \href{https://eudml.org/doc/34081}{\mbox{[Web]}} $
  11. I. J.Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly,66(1959), 361–375. $ \href{https://doi.org/10.1080/00029890.1959.11989303}{\mbox{[CrossRef]}} $