THE D_p^q (∆^+r )-STATISTICAL CONVERGENCE

Neslihan Boztaş, Mehmet Küçükaslan

DOI Number
https://doi.org/10.22190/FUMI2002405B
First page
405
Last page
422

Abstract


Let p(n) and q(n) be nondecreasing sequence of positive integers such that p(n) < q(n) and limn→∞ q(n) = ∞ holds. For any r ∈ Z^+, we define D_p,q^+r- statistical convergence of ∆^+r x where ∆^+r is r- th difference of the sequence (x_n). The main results in this paper consist in determining sets of sequences χ and χ' of the form [D_ p^q]_0 α satisfying χ ⊂ [D_p^q]_0(∆^+r ) ⊂ χ ' and sets φ and φ' of the form [D_p^q]_α satisfying φ ≤ [D_p^q]_∞(∆^+r ) ≤ φ'  .

Keywords

D_p^q (∆^+r )-statistical convergence; summability methods; Deferred Cesaro mean; sequence space.

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References


R. P. Agnew: On deferred Cesaro mean. Ann. Math. 33 (1932), 413–421.

J. S. Connor: The statistical and strong p-Cesaro convergence of sequences. Analysis 8 (1988), 47-63.

B. De Malafosse and M. Mursaleen and V. Rakocevic: The λ +r (µ)-statistical convergence. Ann. Funct. Anal. (2016), 1-15.

M. Et and A. Alotaibi and S. A. Mohiuddine: On (∆ m ,I)- statistical convergence of order α. The Scientific World Journal, (2014).

M. Et and A. Bektas ¸: Generalized strongly (V,λ)-summable sequences defined by Orlicz functions. Math. Slovaca 54 (2004), no. 4, 411-422.

M. Et and R. C¸olak : On some generalized difference sequence spaces. Shoochow J. Math. 21 (1995), 377-386.

M. Et and F. Nuray: ∆ m -statistical convergence. Indian, J. Pure Appl. Math. 32 (2001), 961-969.

M. Et and F. Temizsu and M. C¸ınar: ∆ m -Deferred statistical convergence of order α. Filomat 30 (2016), 667-673.

H. Fast: Sur la convergence statistique. Coll. Math.2 (1951), 241-244.

J. A. Fridy and C. Orhan: Lacunary statistical convergence. Pasific. J. Math. 160 (1993), 43-51.

H. Kızmaz: On certain sequence spaces. Canadian Math. Bull. 24 (1981), 169-176.

M. Küc ¸ükaslan and M. Yilmaztürk: On deferred statistical convergence of sequences. Kyungpook Math. J. 56 (2016), 357-366.

M. Küc ¸ükaslan and M. Yilmaztürk: On strongly deferred Cesaro summability and

deferred statistical convergence of the sequences. Bitlis Eren Univ. J. Sci. Technology 3 (2011), 22-25.

I. J. Maddox : Elements of Functional Analysis. Cambridge University Press, (1967), 345-355.

M. Mursaleen: λ-statistical convergence. Math. Slovaca 50 (2000), 111-115.

H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique. Colloquium Math. vol. 2 (1951), 73-74.

B. Tripathy and M. Et: On generalized difference lacunary statistical convergence. Studia Univ. Babe¸ s-Bolyai Math. 50 (2005), no. 1, 119-130.




DOI: https://doi.org/10.22190/FUMI2002405B

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