The Arzelà-Ascoli theorem by means of ideal convergence
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KünyeTaş, E., Yurdakadim, T. (2018). The Arzelà–Ascoli theorem by means of ideal convergence. Georgian Mathematical Journal, 25(3), 475-479.
In this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà-Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions. © 2018 Walter de Gruyter GmbH, Berlin/Boston.