This paper concerns a generalization of approximately continuous functions, namely S-approximately continuous functions. This notion is associated with S-density points, where S is a sequence of measurable sets tendin...
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This paper concerns a generalization of approximately continuous functions, namely S-approximately continuous functions. This notion is associated with S-density points, where S is a sequence of measurable sets tending to 0. Moreover, we present some properties of these functions and show their connection with measurable functions, functions from the first Baire class, and Darboux functions.
Abstract: Let $\Delta ’$ be the class of all derivatives. The main goal of this paper is the investigation of the vector space generated by $\Delta ’$ and O’Malley’s class $B_1^ \ast$; this space is identi...
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Abstract: Let $\Delta ’$ be the class of all derivatives. The main goal of this paper is the investigation of the vector space generated by $\Delta ’$ and O’Malley’s class $B_1^ \ast$; this space is identical with our system $[\Delta ’]$. We show, in particular, that each approximatelycontinuous function and each approximate derivative belongs to $[\Delta ’]$ and that $[\Delta ’]$ is the system of all functions of the form $g’ + hk’$, where $g$, $h$ and $k$ are differentiable.
In this paper we give the definition of [lambda, rho]-continuity of real-valued functions defined on an open interval, which is an example of path continuity. We give some properties of [lambda, rho]-continuous functi...
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In this paper we give the definition of [lambda, rho]-continuity of real-valued functions defined on an open interval, which is an example of path continuity. We give some properties of [lambda, rho]-continuousfunctions. The aim of the paper is to find the maximal additive class and the maximal multiplicative class for the family of [lambda, rho]-continuousfunctions.
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