Zobrazeno 1 - 10
of 87
pro vyhledávání: '"Won-Gil Park"'
Autor:
Jae-Hyeong Bae, Won-Gil Park
Publikováno v:
AIMS Mathematics, Vol 9, Iss 3, Pp 7084-7094 (2024)
Let $ n $ be an integer greater than $ 1 $. In this paper, we obtained the stability of the multivariable Cauchy-Jensen functional equation $ nf\bigg(x_1+{\cdots}+x_n, \frac {y_1+{\cdots}+y_n}n\bigg) = \sum\limits_{1\le i, j\le n}f(x_i, y_j) $
Externí odkaz:
https://doaj.org/article/3c53b1ebf71f49a09563740a056608db
Publikováno v:
Mathematics, Vol 12, Iss 14, p 2274 (2024)
For the inner product space, we have Appolonius’ identity. From this identity, Park and Th. M. Rassias induced and investigated the quadratic functional equation of the Apollonius type. And Park and Th. M. Rassias first introduced an Apollonius-typ
Externí odkaz:
https://doaj.org/article/92ec36eef8594a1a853e87484e4fb38f
Autor:
Jae-Hyeong Bae, Won-Gil Park
Publikováno v:
Journal of Inequalities and Applications, Vol 2022, Iss 1, Pp 1-19 (2022)
Abstract We investigate the Hyers–Ulam stability of the following cubic–quadratic functional equation relative to elliptic curves f ( x + y + z , u + v + w ) + f ( x + y − z , u + v + w ) + 2 f ( x , u − w ) + 2 f ( y , v − w ) = f ( x + y
Externí odkaz:
https://doaj.org/article/17d110e6117a4ae68bcbc855ab33aa6e
Publikováno v:
Symmetry, Vol 13, Iss 8, p 1313 (2021)
Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is
Externí odkaz:
https://doaj.org/article/5afdd42e599243439bfa9daa9c895eb5
Autor:
Jae-Hyeong Bae, Won-Gil Park
Publikováno v:
Symmetry, Vol 13, Iss 7, p 1180 (2021)
Symmetry is repetitive self-similarity. We proved the stability problem by replicating the well-known Cauchy equation and the well-known Jensen equation into two variables. In this paper, we proved the Hyers-Ulam stability of the bi-additive function
Externí odkaz:
https://doaj.org/article/a0a7a7cd15204374a854840b430e1558
Autor:
Won-Gil Park, Jae-Hyeong Bae
Publikováno v:
Discrete Dynamics in Nature and Society, Vol 2012 (2012)
We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unita
Externí odkaz:
https://doaj.org/article/25c3952e54974cf393f0cfccc5048589
Publikováno v:
Discrete Dynamics in Nature and Society, Vol 2012 (2012)
Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((
Externí odkaz:
https://doaj.org/article/03894c4bba0f49f8bc438c390f26195a
Autor:
Jae-Hyeong Bae, Won-Gil Park
Publikováno v:
Abstract and Applied Analysis, Vol 2012 (2012)
We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its u
Externí odkaz:
https://doaj.org/article/31a346fb331c4505bd38cf49eea5fa96
Autor:
Won-Gil Park, Jae-Hyeong Bae
Publikováno v:
Journal of Inequalities and Applications, Vol 2010 (2010)
We prove the Hyers-Ulam stability of a 2-dimensional quadratic functional equation in a class of vector variable functions in Banach modules over a unital C⋆-algebra.
Externí odkaz:
https://doaj.org/article/1dfa8ec3386d487d85d38ad6f96fb03d
Autor:
Won-Gil Park, Jae-Hyeong Bae
Publikováno v:
Journal of Inequalities and Applications, Vol 2010 (2010)
We obtain the generalized Hyers-Ulam stability of the bi-quadratic functional equation f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4[f(x,z)+f(x,w)+f(y,z)+f(y,w)] in quasinormed spaces.
Externí odkaz:
https://doaj.org/article/d47010635ce44728a4ef12bb4a887297