Banas, Vladislav \(\mathcal I\)-derivative. (English) Zbl 1296.26010 Acta Univ. M. Belii, Ser. Math. 21, 63-70 (2013). 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. Reviewer: Cristinel Mortici (Târgovişte) 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 Keywords:statistical convergence; \(\mathcal{I}\)-convergence; \(\mathcal{I}^{k}\)-convergence; \(\mathcal{I}\)-continuity; \(\mathcal{I}\)-derivative; Dini’s derivatives PDFBibTeX XMLCite \textit{V. Banas}, Acta Univ. M. Belii, Ser. Math. 21, 63--70 (2013; Zbl 1296.26010) Full Text: Link