


Paper's Title:
Relation Between The Set Of Nondecreasing Functions And The Set Of Convex Functions
Author(s):
Qefsere Doko Gjonbalaj and Luigj Gjoka
Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova
Email:
qefsere.gjonbalaj@unipr.edu
Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.
Email: luigjgjoka@ymail.com
Abstract:
In this article we address the problem of integral presentation of a convex function. Let I be an interval in R. Here, using the Riemann or Lebesgue’s integration theory, we find the necessary and sufficient condition for a function f: I→ R to be convex in I.
Paper's Title:
Relations Between Differentiability And Onesided 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.
Email: qefsere.gjonbalaj@unipr.edu
{Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
Email: luigjgjoka@ymail.com
Abstract:
In this paper, we attempt to approach to the problem of connection between differentiation and oneside differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with onesided differentiation, more precisely with righthand 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 righthand 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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