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5: Paper Source PDF document

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.



3: Paper Source PDF document

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 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 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.



1: Paper Source PDF document

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
ąźych 2,
30-084 Krak
w,
Poland
jbrzdek@ap.krakow.pl

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



1: Paper Source PDF document

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.


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