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\(\mathcal I\)-derivative. (English) Zbl 1296.26010

This paper deals with the notion of \(\mathcal{I}\)-convergence of a real function that is a generalization of statistical convergence. The \(\mathcal{I}\)-derivative is introduced based on the notion of \(\mathcal{I}\)-convergence. The relations between the \(\mathcal{I}\)-derivative and Dini’s derivatives and the usual derivative are established.

MSC:

26A03 Foundations: limits and generalizations, elementary topology of the line
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
40A05 Convergence and divergence of series and sequences
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