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On $$F$$-continuity of real functions. (English) Zbl 0788.26004
Summary: The concept of $$F$$-continuity of real functions is based on the well- known notion of almost convergence of sequences of real numbers. From the $$F$$-continuity of a function at a point its linearity follows. This fact strengthens a result of E. Öztürk [Commun. Fac. Sci. Univ. Ankara, Ser. A1 32, 25-30 (1983; Zbl 0597.40001)].

MSC:
 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 40A05 Convergence and divergence of series and sequences
Zbl 0597.40001