


Paper's Title:
A Coincidence Theorem for Two Kakutani Maps
Author(s):
Mircea Balaj
Department of Mathematics,
University of Oradea,
410087, Oradea,
Romania.
mbalaj@uoradea.ro
Abstract:
In this paper we prove the following theorem: Let X be a nonempty compact convex set in a locally convex Hausdorff topological vector space, D be the set of its extremal points and F,T: X―◦X two Kakutani maps; if for each nonempty finite subset A of D and for any x ∈ coA, F (x) ∩ coA ≠ Ø, then F and T have a coincidence point. The proof of this theorem is given first in the case when X is a simplex, then when X is a polytope and finally in the general case. Several reformulations of this result are given in the last part of the paper.
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.
Paper's Title:
Some properties of kquasi class Q* operators
Author(s):
Shqipe Lohaj and Valdete Rexhëbeqaj Hamiti
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Abstract:
In this paper, we give some results of kquasi class Q^{*} operators. We proved that if T is an invertible operator and N be an operator such that N commutes with T^{*}T, then N is kquasi class Q^{*} if and only if TNT^{1} is of kquasi class Q^{*}. With example we proved that exist an operator kquasi class Q^{*} which is quasi nilpotent but it is not quasi hyponormal.
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