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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings
Author(s):
M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi
The Open University of Japan,
Chiba, 261-8586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp
Yamagata University,
Yonezawa 992-8510,
Japan
miura@yz.yamagata-u.ac.jp
Toho University, Yamagata University,
Chiba, 273-0866,
Japan
sin_ei1@yahoo.co.jp
Abstract:
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.
Paper's Title:
Stability of Almost Multiplicative Functionals
Author(s):
Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi
Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,
Japan
Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,
Japan
Department of Applied Mathematics and Physics, Graduate School of
Science and Engineering,
Yamagata University,
Yonezawa 992-8510
Japan
oka@mx.ibaraki.ac.jp
miura@yz.yamagata-u.ac.jp
sin-ei@emperor.yz.yamagata-u.ac.jp
Abstract:
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 p≠1, 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.
Paper's Title:
On Interaction of Discontinuous Waves in a Gas with Dust Particles
Author(s):
J. Jena
Department of Mathematics, Netaji Subhas institute of technology,
Sector-3, Dwarka, New Delhi - 110 075,
India.
jjena67@rediffmail.com
jjena@nsit.ac.in
Abstract:
In this paper, the interaction of the strong shock with the weak discontinuity has been investigated for the system of partial differential equations describing one dimensional unsteady plane flow of an inviscid gas with large number of dust particles. The amplitudes of the reflected and transmitted waves after interaction of the weak discontinuity through a strong shock are evaluated by exploiting the results of general theory of wave interaction.
Paper's Title:
On a Method of Proving the Hyers-Ulam Stability
of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchor
Abstract:
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
Paper's Title:
The Conservativeness of Girsanov Transformed for Symmetric Jump-diffusion Process
Author(s):
Mila Kurniawaty and Marjono
Department of Mathematics,
Universitas Brawijaya,
Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id,
marjono@ub.ac.id
Abstract:
We study about the Girsanov transformed for symmetric Markov processes with jumps associated with regular Dirichlet form. We prove the conservativeness of it by dividing the regular Dirichlet form into the "small jump" part and the "big jump" part.
Paper's Title:
Conservativeness Criteria of Girsanov Transformation for Non-Symmetric Jump-diffusion
Author(s):
Mila Kurniawaty
DDepartment of Mathematics,
Universitas Brawijaya, Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id
Abstract:
We develop the condition in our previous paper [The Conservativeness of Girsanov transformed for symmetric jump-diffusion process (2018)] in the framework of nonsymmetric Markov process with jumps associated with regular Dirichlet form. We prove the conservativeness of it by relation in duality of Girsanov transformed process and recurrent criteria of Dirichlet form.
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