


Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
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 2homogeneous 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:
Hankel Operators on Copson's Spaces
Author(s):
Nicolae Popa
Institute of Mathematics of Romanian Academy,
P.O. BOX 1764
RO014700 Bucharest,
Romania.
Email: Nicolae.Popa@imar.ro, npopafoc@gmail.com
Abstract:
We give a characterization of boundedness of a Hankel matrix, generated by a pozitive decreasing sequence, acting on Copson's space cop(2).
Paper's Title:
A general common fixed point theorem for reciprocally continuous mappings satisfying an implicit relation
Author(s):
A. Djoudi and A. Aliouche
Faculty of Science, University of Annaba,
P.O. Box 23000, Annaba,
Algeria.
adjoudi@yahoo.com
Department of Mathematics, University of Larbi Ben M'Hidi,
OumElBouaghi 04000,
Algeria.
abdmath@hotmail.com
Abstract:
A general common fixed point theorem for compatible mappings satisfying an implicit relation is obtained by replacing the continuity of one mapping by the reciprocal continuity of two mappings.
Paper's Title:
On a Method of Proving the HyersUlam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the HyersUlam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and realvalued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Semivectorial Bilevel Optimization on AffineFinslerMetric Manifolds
Author(s):
Faik Mayah^{1}, Ali S Rasheed^{2} and Naseif J. Al Jawari^{3}
^{1}Department of Physics,
College of Sciences,
University of Wasit,
Iraq.
Email: faik.mayah@gmail.com
^{2}Ministry of Higher Education and Scientific Research,
Iraq.
Email: ali.math2018@yahoo.com
ahmedhashem@gmail.com
^{3}Dept.
of Mathematics,
College of Science,
Mustansiriyah University, Baghdad,
Iraq.
Email: nsaif642014@yahoo.com
Abstract:
A Finsler manifold is a differential manifold together with a Finsler metric, in this paper we construct a new class of Finsler metric affine manifolds on bilevel semivectorial with optimization problems. The first steps for this purpose involve the study of bilevel optimization on affine manifolds. The bilevel programming problem can be viewed as a static version of the noncooperative, twoperson game which was introduced in the context of unbalanced economic markets. Bilevel optimization is a special kind of optimization where one problem is embedded within another.
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