Abstract
This paper interprets the relationship between the statistical Cesàro summability method and statistical convergence for sequences in intuitionistic fuzzy normed spaces. There are several studies in the literature on the Cesàro summability method and its statistical version, in classical, fuzzy, and intuitionistic fuzzy normed spaces. However, what distinguishes this study from others, besides the techniques used, is that it is a more comprehensive research in terms of both the space being studied and the path to the statistical convergence from the statistical Cesàro summability method. Our primary goal in this work is to investigate whether conditions designated as O-type like q-boundedness and statistical slow oscillation require statistical Cesàro summable sequences be statistical convergent with respect to the intuitionistic fuzzy norm \((\mu ,\nu ).\) Moreover, we inquire about the existence of a more inclusive condition than these conditions, from which we can derive a similar inference. Our second aim is to present a series of auxiliary results designed to be utilized in the proofs of our main results. To go into a little detail, we discuss some algebraic properties of statistical limits, including additivity and homogeneity, as well as the existence of a statistical limit of subsequences and moving averages of a sequence. Finally, we give some examples of the application of the intuitionistic fuzzy normed space in engineering, in order to extend the area of influence of the relevant space and to support the studies carried out in the context of this space.
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The authors thank the anonymous reviewers for their insightful and valuable suggestions, and for their constructive comments, which contributed significantly to improving the article in its present form. The authors thank the Editor-in-Chief and the Associate Editor of the journal for their valuable feedback and comments.
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Önder, Z., Karakahya, S. & Çanak, İ. Tauberian theorems for the statistical Cesàro summability method in intuitionistic fuzzy normed spaces. Soft Comput 28, 87–104 (2024). https://doi.org/10.1007/s00500-023-09335-x
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DOI: https://doi.org/10.1007/s00500-023-09335-x