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Hence statistical convergence implies logarithmic statistical convergence.
The concept of λ-statistical convergence of order α is a generalization of the concepts of statistical convergence, λ-statistical convergence, and statistical convergence of order α.
Fridy [34] gave characterizations of statistical convergence.
If (p_{k}=1) for all k then weighted statistical convergence is reduced to statistical convergence.
In case (alpha= 1), the statistical convergence of order α reduces to the statistical convergence.
The statistical convergence of order α is same with the statistical convergence for α = 1.
Theorem 2.1 Statistical convergence implies logarithmic statistical convergence but converse need not be true.
In [2] Schoenberg gave some basic properties of statistical convergence.
Savaş [8] studied statistical convergence in random 2-normed space.
Statistical convergence has recently become an area of active research.
The theory of statistical convergence has been introduced in [6].
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