Abstract
In this paper, we have introduced the extension of recently introduced notion of summability of lacunary statistical delta 2 quasi Cauchy sequences to double sequences and established some essential results using analogy.
Highlights
The concept of statistical convergence was formally introduced by Fast [8] and Schoenberg [18] independently
Statistical convergence was introduced over fifty years ago, it has become an active area of research in recent years
It has been applied in various areas such as summability theory (Fridy [9] and Salat [15]), topological groups (Cakalli [1], [4]), topological spaces (Maio and Kocinac [10]), locally convex spaces (Maddox [11]), measure theory (Cheng et al [5]), (Connor and Swardson [6]) and (Miller [12]), Fuzzy Mathematics (Nuray and Savas [14] and Savas [25])
Summary
The concept of statistical convergence was formally introduced by Fast [8] and Schoenberg [18] independently. Definition 1.1: ([13]): A real double sequence x = (xjk) is statistically convergent to a number l if for each ε > 0, the set 2. MAIN RESULTS A double sequence (xjk) in R is called double lacunary statistically 2-quasi-Cauchy if Sθr,s − lim ∆xj,k = 0, where ∆xj,k = xj+1,k+1 − xj,k for each positive integers j, k.
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