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JOHN MICHAEL RASSIAS,HEMEN DUTTA,NARASIMMAN PASUPATHI 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.2
The aim of this article is to study the Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability in non-Archimedean Intuitionistic fuzzy normed spaces. The paper introduces a new A- quartic functional equation and obtain solution for the same functional equation. Further, stability problem is investigated for the newly intro- duced A-quartic functional equation in non-Archimedean intuitionistic fuzzy normed spaces.
ON A GENERALIZED TRIF'S MAPPING IN BANACH MODULES OVER A C*-ALGEBRA
Park, Chun-Gil,Rassias Themistocles M. Korean Mathematical Society 2006 대한수학회지 Vol.43 No.2
Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<...<i_k{\leq}mn}\;f(\frac {x_{i_1}+...+x_{i_k}} {k})$$ if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.
APPROXIMATELY ADDITIVE MAPPINGS OVER p-ADIC FIELDS
Choon kil Park,Deok Hoon Boo,Themistocles M.Rassias 충청수학회 2008 충청수학회지 Vol.21 No.1
In this paper, we prove the Hyers{Ulam{Rassias sta-bility of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation 2f( x+y2 ) = f(x) + f(y) over the p-adic ¯eld Qp. The concept of Hyers{Ulam{Rassias stability orig-inated from the Th.M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297{300.
Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces
Rassias, J.M.,Kim, H.M. Academic Press 2009 Journal of mathematical analysis and applications Vol.356 No.1
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces.
Moradlou, Fridoun,Rassias, Themistocles M. Korean Mathematical Society 2013 대한수학회보 Vol.50 No.6
In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.
Fridoun Moradlou,Themistocles M. Rassias 대한수학회 2013 대한수학회보 Vol.50 No.6
In this paper, we investigate the generalized HyersUlam– Rassias stability of the following additive functional equation [수식] in quasi-β-normed spaces.
Dongwen Zhang,JOHN MICHAEL RASSIAS,Yongjin Li 강원경기수학회 2022 한국수학논문집 Vol.30 No.4
By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.
REFINED HYERS{ULAM STABILITY FOR JENSEN TYPE MAPPINGS
John Michael Rassias,Ju ri Lee,Hark Mahn Kim 충청수학회 2009 충청수학회지 Vol.22 No.1
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we improve results for Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative Jensen type mappings.