Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α

Abstract

In the paper [32], we have defined the concepts of lacunary statistical convergence of order α and strong N θ p −summability of order α for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order α and strong N θ p −summability of order α.

On (f, I) - Lacunary statistical convergence of Order α of sequences of sets

“…Schoenberg [32] established some basic properties of statistical convergence and studied the concept as a summability method. Later on it was further investigated from the sequence space point of view and linked with summability theory by Altınok et al ( [2], [3]), Bhardwaj and Dhawan [4], Caserta et al [5], Ç ınar et al [9], Connor [12], Ç akallı et al ( [6], [7], [8]), Ç olak et al ( [10], [11], [23]), Et et al ( [13], [14], [15], [16]), Fridy [19], Gadjiev and Orhan [21], Işık and Akbaş [22], Salat [29], Savaş and Et [31], Şengül [34], Taylan [38], and many others. Nuray and Rhoades [28] extended the notion to statistical convergence of sequences of sets and gave some basic theorems.…”

On Asymptotically Lacunary Statistical Equivalent Sequences of Orderαin Probability

“…Throught this paper the intervals determined by θ will be denoted by I r = (k r−1 , k r ] and the ratio k r k r−1 will be abbreviated by q r . Recently lacunary sequences have been studied in ( [8], [10], [12], [20]). …”

Asymptotically Statistical Equivalent of Orderαin Amenable Semigroups

“…al. ([8], [9], [10], [11], [12]), Fridy [14], Işık [15], Küçükaslan and Yılmaztürk [16], Mursaleen [20], Nuray and Rhoades ( [22], [23], [24]), Salat [26], Sengül and Et [28] and many others.…”