Abstract
The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α. We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.
Highlights
The idea of statistical convergence was given by Zygmund [45] in the ...rst edition of his monograph published in Warsaw in 1935
The concept of statistical convergence was introduced by Steinhaus [42] and Fast [20] and later reintroduced by Schoenberg [38]
Over the years and under di¤erent names statistical convergence was discussed in the theory of Fourier analysis, Ergodic theory, Number theory, Measure theory, Trigonometric series, Turnpike theory and Banach spaces
Summary
The idea of statistical convergence was given by Zygmund [45] in the ...rst edition of his monograph published in Warsaw in 1935. Sengül and Et ([19],[39]) generalized the concepts such as lacunary statistical convergence of order and lacunary strong p Cesàro summability of order for sequences of real numbers. Di¤erence sequence spaces was de...ned by K¬zmaz [27] and the concept was generalized by Et et al ([14],[18]) as follows: m (X) = fx = (xk) : ( mxk) 2 Xg ; where X is ( mxk) =
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