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The statistical convergence of order α is defined as follows.
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.
The results show exponential error convergence of order p + 1∕2 for smooth solutions.
In case (alpha= 1), the statistical convergence of order α reduces to the statistical convergence.
The convergence of order for the sequence of iterates is also established.
Bhardwaj and Dhawan [36] continued this work and defined f-statistical convergence of order α.
In this paper we define and study λ-double almost statistical convergence of order α.
The double statistical convergence of order α is defined as follows.
For (f(x) = x), (S_{alpha}^{f} -convergence becomes statistical convergence of order α.
In this paper, we define and study lacunary double almost statistical convergence of order α.
We now introduce a new concept of f-statistical convergence of order α as follows.
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