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 Non-decreasing 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

E-mail: qefsere.gjonbalaj@uni-pr.edu
 

Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.

E-mail: 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 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.

Paper's Title:

Some properties of k-quasi 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.
E-mail: shqipe.lohaj@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

Abstract:

In this paper, we give some results of k-quasi 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 k-quasi class Q^* if and only if TNT^-1 is of k-quasi class Q^*. With example we proved that exist an operator k-quasi class Q^* which is quasi nilpotent but it is not quasi hyponormal.

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