I−lacunary Statistical Convergence of Order Β of Difference Sequences of Fractional Order

Abstract

In this paper, we introduce the concepts of ideal ∆α−lacunary statis- tical convergence of order β with the fractional order of α and ideal ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1and α be a fractional order) and give some relations about these concepts.

Lacunary Statistical Convergence of Order Α in Partial Metric Spaces

“…The concept of statistical convergence has been approached from various angles, and various definitions of convergence have been provided. For further reading on some recent relevant studies on lacunary statistical convergence, see [1], [2] and [16].…”

On harmonic summability of order α

“…1: The intervals determined by is denoted by I r = (k r 1 ; k r ] and the ratio kr k r 1 is abbreviated by q r , and q 1 = k 1 for convenience. Lacunary convergence was studied in ( [4], [12], [14]).…”

On ρ-statistical convergence of order α of sequences of sets

“…Schoenberg [28] 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 [1], Aral et al ( [2,3]), Bhardwaj and Dhawan [5], C ¸akallı et al ( [6][7][8]), Caserta et al [9], C ¸ınar et al [10], Connor [12], C ¸olak [11], Demirci et al [13], ), Fridy [19], Gadjiev and Orhan [20], Is ¸ık and Akbas ¸ [21], Salat [26], Savas and Et [27], S ¸engül [29] and many others. Let (X, σ) be a metric space.…”