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4: Paper Source PDF document

Paper's Title:

Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings


M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi

The Open University of Japan,
Chiba, 261-8586,

 Yamagata University,
Yonezawa 992-8510,

Toho University, Yamagata University,
Chiba, 273-0866,


We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.

3: Paper Source PDF document

Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results


Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,

2DST-NRF 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


The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

2: Paper Source PDF document

Paper's Title:

Stability of Almost Multiplicative Functionals


Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi

Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,

Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,

Department of Applied Mathematics and Physics, Graduate School of Science and Engineering,
Yamagata University,
Yonezawa 992-8510


Let δ and p be non-negative real numbers. Let be the real or complex number field and a normed algebra over . If a mapping satisfies

then we show that φ is multiplicative or for all If, in addition, φ satisfies

for some p1, then by using Hyers-Ulam-Rassias stability of additive Cauchy equation, we show that φ is a ring homomorphism or for all In other words, φ is a ring homomorphism, or an approximately zero mapping. The results of this paper are inspired by Th.M. Rassias' stability theorem.

1: Paper Source PDF document

Paper's Title:

On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains


Janusz Brzdęk

Department of Mathematics
 Pedagogical University Podchor
ąźych 2,
30-084 Krak


We show that generalizations of some (classical) results on the Hyers-Ulam 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

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