## On the $$\mathcal{A}$$-continuity of real functions.(English)Zbl 0880.26006

Let $$A$$ be a regular matrix. A function $$f:\mathbb{R}\to\mathbb{R}$$ is said to be $$A$$-continuous at $$x_0\in\mathbb{R}$$ provided that $$A$$-$$\lim x_n=x_0$$ implies $$A$$-$$\lim f(x_n)= f(x_0)$$ [cf. J. Antoni and T. Šalát, Acta Math. Univ. Comenianae 39, 159-164 (1980; Zbl 0519.40006)]. In connection with the $$A$$-continuity of functions, the authors introduce the concept of $${\mathcal A}$$-continuity of functions replacing the matrix $$A$$ by a sequence $${\mathcal A}= (A^i)$$ of matrices. In the paper, sufficient conditions are given for usual continuity, linearity and constancy of functions that are $${\mathcal A}$$-continuous at a point $$x_0\in\mathbb{R}$$.

### MSC:

 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable

### Keywords:

$${\mathcal A}$$-continuity; linearity; constancy

Zbl 0519.40006