Paranormlu Uzaylarda α. Dereceden Deferred İstatistiksel Yakınsaklık

Yıl 2023, , 1 - 6, 30.06.2023

Haşmet Kapşigay , Muhammed Çınar

https://doi.org/10.18586/msufbd.1188106

Öz

Bu çalışmanın amacı paranormlu uzaylarda α. dereceden deferred istatistiksel yakınsaklık, paranormlu uzaylarda α. dereceden deferred istatistiksel Cauchy dizisi tanımları ile paranormlu uzaylarda deferred Cesáro yakınsaklık tanımını verip bunlar arasındaki ilişkiyi incelemektir.

Anahtar Kelimeler

Cesáro Ortalaması, Deferred Cesáro Ortalaması, Deferred İstatistiksel Yakınsaklık, İstatistiksel Yakınsaklık

Deferred Statistical Convergence of Order α in Paranormed Space

Öz

This study aims to define deferred statistical convergence of α. order in paranorm spaces, the definitions of deferred statistical Cauchy convergence of α. order in paranorm spaces and the definition of diferred Cesáro in paranorm spaces and to investigate the relation among these.

Anahtar Kelimeler

Cesáro Means, Deferred Cesáro Mean, Deferred Statistical Convergence, Statistical Convergence

Kaynakça

• Zygmund A. Trigonometric series, Cambridge University Press, Cambridge, 1979.
• Steinhaus, H. Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum. 2 73-74, 1951.
• Fast, H. Sur la convergence statistique, Colloquium Mathematicum. 2 241- 24, 1951.
• Schoenberg, I. J. The integrability of certain functions and related summability methods II, The American Mathematical Monthly. 66 562-563, 1959.
• Connor, J. The statistical and strong p-Cesaro convergence of sequences, Analysis. 8 47-64, 1988. Fridy, J. A. On statistical convergence, Analysis. 5 301-314, 1985. Altundağ, S., Başarır M. Lacunary statistical convergence in a paranormed space, AIP Conference Proceedings, 1479- 929, 2012.
• Çolak, R., Bektaş, Ç. A. λ-statistical convergence of order α, Acta Mathematica Scientia Series B. 31 953-959, 2011.
• Mursaleen M. λ-statistically convergence Mathematica Slovaca. 50 111-115, 2000.
• Cinar M., Karakas M., Et, M. On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory and Applications. 33 1–11 2013.
• Şengül, H., Et, M. On lacunary statistical convergence of order α. Acta Mathematica Scientia. 34 473–482, 2014.
• Wilansky, A. Summability through functional analysis, North Holland, 1984.
• Niven, I., Zucherman, H. S. and Montgomery H. L. An introduction to the theory of numbers, John Wiley, New York, 1991.
• Çolak, R. Statistical convergence of order α, Modern methods in analysis and its applications, İndia: Anamaya Pub., New Delhi, 121-129, 2010.
• Alotaibi, A., Alroqi, A. M. Statistical convergence in a paranormed space, Journal of Inequalities and Applications. 39 1-6, 2012.
• Ercan, S. On the statistical convergence of order α in paranormed space, Symmetry. 10 483-492, 2018.
• Maddox, I. Elements of functional analysis, Cambiridge University press, 1970.
• Agnew, R. P. On deferred Cesaro means, Annals of Mathematics. 33 413-421, 1932.
• Küçükaslan, M., Yılmaztürk, M. On deferred statistical convergence of sequences, Kyungpook Mathematical Journal. 56 357-366, 2016.
• Alghamdi, M. A., Mursaleen, M., λ-statistical convergence in paranormed space, Abstract and Applied Analysis. Art. ID 264520. 1-5 2013.