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6: Paper Source PDF document

Paper's Title:

Positive Solutions of Evolution Operator Equations

Author(s):

Radu Precup

Department of Applied Mathematics,
Babes-Bolyai University,
Cluj, Romania

Abstract:

Existence and localization results are derived from Krasnoselskiiís compressionexpansion fixed point theorem in cones, for operator equations in spaces of continuous functions from a compact real interval to an abstract space. The main idea, first used in [12], is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskiiís theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. An application is presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain.



1: Paper Source PDF document

Paper's Title:

A relation between nuclear cones and full nuclear cones

Author(s):

G. Isac and A. B. Nemeth

Department of Mathematics,
Royal Military College of Canada,
P. O. Box 17000 STN Forces Kingston, Ontario,
Canada K7K 7B4.
isac-g@rmc.ca

Faculty of Mathematics and Computer Science,
Babes-Bolyai University,
3400 Cluj-Napoca,
Romania.
nemab@math.ubbcluj.ro


Abstract:

The notion of nuclear cone in locally convex spaces corresponds to the notion of well based cone in normed spaces. Using the bipolar theorem from locally convex spaces it is proved that every closed nuclear cone is a full nuclear cone. Thus every closed nuclear cone can be associated to a mapping from a family of continuous seminorms in the space to the topological dual of the space. The relation with Pareto efficiency is discussed.



1: Paper Source PDF document

Paper's Title:

Some GrŁss Type Inequalities in Inner Product Spaces

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa

URL: http://rgmia.org/dragomir 

Abstract:

Some inequalities in inner product spaces that provide upper bounds for the quantities

and  ,

where e,f ∈ H with and x,y are vectors in H satisfying some appropriate assumptions are given. Applications for discrete and integral inequalities are provided as well.



1: Paper Source PDF document

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1

1Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

2Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.


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