Lacunary Statistical Summability

Fridy, J. A.; Orhan, Cihan

doi:10.1006/jmaa.1993.1082

Cited by 128 publications

(70 citation statements)

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“…In this case we write stat-lim x k = L. The idea of statistical convergence for sequence of real numbers was studied by F a s t [4] and S c h o e n b e r g [16] at the initial stage. Later on it was studied from sequence space point of view and linked with summability methods by S a lá t [15], F r i d y [5], F r i d y and O r h a n [6], T r i p a t h y [18] and many others.…”

Section: Statistical Convergencementioning

confidence: 99%

Strongly almost convergent generalized difference sequences associated with multiplier sequences

Eşi

Tripathy

2007

Mathematica Slovaca

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Section: Statistical Convergencementioning

confidence: 99%

Strongly almost convergent generalized difference sequences associated with multiplier sequences

Eşi

Tripathy

2007

Mathematica Slovaca

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“…We now recall lacunary statistical convergence, introduced in [12] and [13], that can be regarded as a special case of A-statistical convergence. A lacunary sequence is an increasing sequence of positive integers 6 = {k r } such that ko = 0 and h r := k r -k T -1 -> 00 as r -> 00 and we set I r := (k r -i,k r ) and q T := k T /k r -\.…”

Section: K£kmentioning

confidence: 99%

“…The number sequence x = (xjb) is said to be lacunary statistically convergent to L (See, [12], [13]) provided that for every e > 0 lim-^|{A;eJ r :|x fc -X|>e}| = 0. (0, otherwise.…”

Section: K£kmentioning

confidence: 99%

On Lacunary Statistical Limit Points

Demirci¹

2002

Demonstratio Mathematica

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Abstract. In this paper we study the concepts of lacunary statistical limit points and lacunary statistical cluster points as well as the concept of lacunary statistical core for a bounded complex number sequence. Introduction and NotationsThe idea of statistical convergence was first introduced by Steinhaus [20] in 1949 and studied by Fast and several authors [7], [10], [2].Recall that a number sequence x = (xfc) is said to be statistically convergent to the number L if for every e > 0, lim -|{fc e}| = 0, n n where the vertical bars indicate the number of elements in the enclosed set.If if is a subset of the natural numbers N, K n will denote the set {k < n : k € K}, and \K n \ will denote the cardinality of K n . The natural density of K [19] is given by 6(K) :-lim-|A" n |, if it exsits. The number sequence n n x -(%k) is statistically convergent to L provided that for every c > 0 the set K(e) := {fc € N : |x fc -L\ > e} has natural density zero [7], [10]. Hence x = (xfc) is statistically convergent to L iff {C\XK(t))n -> 0, (as ra -» oo, for every e > 0), where C\ is the Cesaro mean of order one and XK(<.) is the chsiracteristic function of the set K(e).Statistical convergence can be generalized by using a nonnegative regular matrix A in place of C\: we say that a subset K of N has yl-density This research was supported by Kirikkale University, Turkey. 1991 Mathematics Subject Classification: Primary 40A05, Secondary 26A03, 11B05. Key words and phrases-, lacunary statistical limit point, lacunary statistical cluster point, lacunary statistical core of a sequence.

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“…In [23], Mursaleen and Mohiuddine introduced the concept of lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. Some work on lacunary statistical convergence can be found in [2], [10], [19], [25]. In the recent years, generalization of statistical convergence have appeared in the study of strong integral summability and the structure of ideals of bounded continuous functions on Stone-Cech compactification of the natural numbers.…”

Section: Introductionmentioning

confidence: 99%