Çift diziler için αβ-istatistiksel E-yakınsaklık

Bu makalede, tam sayı ikilileri için verilen yoğunluk kavramının bir genelleştirilmesi olan αβ doğal yoğunluk kavramını tanımladık. Bu yoğunluk kavramı yardımıyla çift diziler için αβ-istatistiksel E-yakınsaklık kavramı tanıtıldı. Daha sonra bu tip yakınsaklığın temel özellikleri incelendi. Ayrıca, E-anlamında αβ-istatistiksel alt limit ve üst limit kavramlarını tanımladık. Son olarak bu kavramlarla ilgili teoremler verdik.

Anahtar Kelimeler:

Çift dizi, E-yakınsaklık, İstatistiksel Yakınsaklık, αβ-istatistiksel E-yakınsaklık, αβ-istatistiksel E-alt limit ve üst limit

Modification of Coupled Drinfel’d-Sokolov-Wilson Equation and Approximate Solutions by Optimal Perturbation Iteration Method

PDF

___

Aktuğlu, H. 2014. Korovkin type approximation theorems proved via αβ-statistical convergence. Journal of Computational and Applied Mathematics, 259, 174--181.
Boos, J., Leiger, T. and Zeller, K. 1997. Consistency theory for SM-methods. Acta Mathematica Hungarica, 76, 83--116.
Çakan, C. and Altay, B. 2006. Statistically boundedness and statistical core of double sequences. Journal of Mathematical Analysis and Applications, 317, 690--697.
Edely, O. H. H. and Mursaleen, M. 2006. Tauberian theorems for statistically convergent double sequences. Information Sciences, 176, 875--886.
Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241--244.
Fridy, J. A. and Orhan, C. 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society, 125(12), 3625--3631.
Hardy, G. H. 1917. On the convergence of certain multiple series. Mathematical Proceedings of the Cambridge Philosophical Society, 19, 86--95.
Karaisa A. 2016. Statistical αβ-Summability and Korovkin Type Approximation Theorem. Filomat, 30(13), 3483--3491.
Móricz, F. 2003. Statistical convergence of multiple sequences. Archiv der Mathematik (Basel), 81(1), 82--89.
Mursaleen, M. and Edely, O. H. H. 2003. Statistical convergence of double sequences. Journal of Mathematical Analysis and Applications, 288, 223--231.
Pringsheim, A. 1898. Elementare theorie der unendliche doppelreihen. Sitsungs berichte der Math. Akad. der Wissenschafftenzu Münch. Ber., 7, 101--153.
Sever, Y. and Talo, Ö. 2014. e-core of double sequences. Acta Mathematica Hungarica, 144(1), 236--246.
Sever, Y. and Talo, Ö. 2017. Statistical e-convergence of double sequences and its application to Korovkin type approximation theorem for functions of two variables. Iranian Journal of Science and Technology. Transaction A. Science, 41(3), 851--857.
Sever, Y. and Talo, Ö. 2018. On statistical e-convergence of double sequences. Iranian Journal of Science and Technology. Transaction A. Science, 42(4), 2063--2068.
Zeltser, M. 2001. Investigation of double sequence spaces by soft and hard analitical methods. Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, (Tartu).
Zeltser, M. 2002. On conservative matrix methods for double sequence spaces. Acta Mathematica Hungarica, 95(3), 225--242.