Kesirli Fark Operatörü ile Elde Edilen Dizilerin Bazı Cesàro-Tipi Toplanabilirliği ve İstatistiksel Yakınsaklığı

Bu çalışmada, reel (ya da kompleks) değerli dizilerin kuvvetli ( , ) p   -Cesàro toplanabilmesi ve ∆?istatistiksel yakınsaklığı verilmiştir. ∆?-istatistiksel yakınsaklık ve kuvvetli ( , ) p   -Cesàro toplanabilme arasındaki bazı kapsama ilişkiler incelenmiştir. Ayrıca ( , ) p wf   ve () S   uzayları arasındaki bazı kapsama bağıntıları verilmiştir.

Some Cesàro-Type Summability and Statistical Convergence of Sequences Generated by Fractional Difference Operator

In this paper, strong ( , ) p   -Cesàro summability and ∆?-statistical convergence are introduced for real (or complex) valued sequences. Some inclusion relations between the ∆?-statistical convergence and strong ( , ) p   -Cesàro summability are examined. Further inclusion relations between the spaces ( , ) p wf   and () S   are introduced.

PDF

___

Altın, Y., 2009. Properties of some sets of sequences defined by a modulus function. Acta Mathematica Scientia. Series B. English Edition, 29(2), 427-434.
Altın, Y., Altınok, H., Çolak, R., 2015. Statistical convergence of order  for difference sequences. Quaestiones Mathematicae, 38, no. 4, 505-514.
Baliarsingh, P., 2013. Some new difference sequence spaces of fractional order and their dual spaces. Journal Applied Mathematics and Computation, 219(18), 9737-9742.
Baliarsingh, P., Dutta, S., 2015. A unifying approach to the difference operators and their applications. Boletim da Sociedade Paranaense de Matemática, 33 (1), 49-56.
Baliarsingh, P., Dutta, S., 2015. On the classes of fractional order difference sequence spaces and their matrix transformations. Applied Mathematics and Computation, 250, 665-674.
Bektaş, Ç.A., Et, M., Çolak R., 2004. Generalized difference sequence spaces and their dual spaces. Journal of Mathematical Analysis and Applications, 292, 423-432.
Bektaş, Ç.A., Et, M., 2006. The dual spaces of the sets of difference sequences of order m. Journal of Inequalities in Pure and Applied Mathematics, 7 (3).
Connor, J.S., 1988. The Statistical and Strong p Cesáro Convergence of Sequená. Analysis, 8, 47-63.
Edely, O.H.H., Mursaleen, M., 2009. On statistical A-summability. Mathematical and Computer Modelling, 49(3-4), 672-680.
Et, M., Çolak, R. 1995. On some generalized difference sequence spaces. Soochow Journal of Mathematics, 21, 377-386.
Et, M., 2000. On some topological properties of generalized difference sequence spaces. International Journal of Mathematics and Mathematical Sciences, 24, 785-791.
Et, M., Nuray, F., 2001. ∆?-statistical convergence. Journal of Pure and Applied Mathematics, 32, 961969.
Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2 241-244.
Fridy, J., 1985. On statistical convergence. Analysis, 5, 301-313.
Işık, M., 2004. On statistical convergence of generalized difference sequences. Soochow Journal of Mathematics, 30(2), 197-205.
Kadak, U., 2015. Generalized lacunary statistical difference sequence spaces of fractional order. International Journal of Mathematics and Mathematical Sciences, Art. ID 984283, 6 pp.
Kızmaz, H., 1981. On certain sequence spaces. Canadian Mathematical Bulletin, 24(2), 169-176.
Nakano, H., 1953. Modular sequence spaces. Proceedings of the Japan Academy, 27, 508-512.
Salat, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150
Schoenberg, I.J., 1959. The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66, 361-375.
Steinhaus, H., 1951. Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum, 2, 73-74.
Zygmund, A., 1979. Trigonometric Series, Cambridge University Press, Cambridge.