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Paper's Title:

Power and Euler-Lagrange Norms

Author(s):

Mohammad Sal Moslehian and John Michael Rassias

Department of Mathematics,
Ferdowsi University,
P. O. Box 1159, Mashhad 91775,
Iran;
Department of Pure Mathematics,
University of Leeds,
Leeds LS2 9JT,
United Kingdom.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/

Pedagogical Department, E.E., Section of Mathematics and Informatics
National and Capodistrian University of Athens,
4, Agamemnonos str., Aghia Paraskevi, Attikis 15342, Athens,
Greece.
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/

Abstract:

We introduce the notions of power and Euler-Lagrange norms by replacing the triangle inequality, in the definition of norm, by appropriate inequalities. We prove that every usual norm is a power norm and vice versa. We also show that every norm is an Euler-Lagrange norm and that the converse is true under certain condition.

Paper's Title:

q-Norms are Really Norms

Author(s):

H. Belbachir, M. Mirzavaziri and M. S. Moslehian

USTHB, Faculté de Mathématiques,
B.P. 32, El Alia, 16111,
Bab Ezzouar, Alger,
Algérie.
hbelbachir@usthb.dz

Department of Mathematics,
Ferdowsi University, P. O. Box 1159,
Mashhad 91775, Iran.
mirzavaziri@math.um.ac.ir
URL: http://www.mirzavaziri.com

Department of Mathematics,
Ferdowsi University,
P. O. Box 1159,
Mashhad 91775, Iran.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/

Abstract:

Replacing the triangle inequality, in the definition of a norm, by , we introduce the notion of a q-norm. We establish that every q-norm is a norm in the usual sense, and that the converse is true as well.

Paper's Title:

Differentiability of Distance Functions in p-Normed Spaces

Author(s):

M. S. Moslehian, A. Niknam, S. Shadkam Torbati

Abstract:

The farthest point mapping in a p-normed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly p-Gateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a Hahn--Banach type theorem in $p$-normed spaces is proved.

Paper's Title:

Stability of a Pexiderized Equation

Author(s):

Maryam Amyar

Department of Mathematics,
Islamic Azad University, Rahnamaei Ave,
Mashhad 91735, Iran,
and Banach Mathematical Research Group (BMRG)
amyari@mshdiau.ac.ir

URL: http://amyari.mshdiau.ac.ir

Abstract:

The aim of the paper is to prove the stability of the Pexiderized equation f(x)=g(y+x)-h(y-x), for any amenable abelian group.

Paper's Title:

A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

Abstract:

A reverse of the triangle inequality in inner product spaces related to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given.

Paper's Title:

On Stan Ulam and his Mathematics

Author(s):

Krzysztof Ciesielski and Themistocles M. Rassias

Mathematics Institute, Jagiellonian University,
Łjasiewicza 6, 30-348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr

Abstract:

In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.

Paper's Title:

Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions

Author(s):

Árpád Száz

Abstract:

By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.

Paper's Title:

On Pseudo Almost Periodic Solutions to Some Neutral Functional-Differential Equations

Author(s):

Toka Diagana and Eduardo Hernández

Department of Mathematics, Howard University
2441 6th Street NW, Washington DC 20059,
USA.
tdiagana@howard.edu