Paper Title:

Relations Between Differentiability And One-sided Differentiability

Author(s):

Q. D. Gjonbalaj, V. R. Hamiti and L. Gjoka

Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
E-mail: qefsere.gjonbalaj@uni-pr.edu

{Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
E-mail: luigjgjoka@ymail.com

Abstract:

In this paper, we attempt to approach to the problem of connection between differentiation and one-side differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with one-sided differentiation, more precisely with right-hand differentiation, we give the generalization of a theorem having to do with Lebesgue’s integration of derivative of a function. Next, based on this generalized result it is proven that if a continuous function has bounded right-hand derivative, then this function is almost everywhere differentiable, which implies that the set of points where the function is not differentiable has measure zero.

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