• 충청수학회지
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• 제22권1호
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• pp.101-116
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• 2009

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.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• 대한수학회보
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• 제46권1호
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• pp.11-23
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the functional inequalities associated with additive functional mappings. Also, we find the solution of these inequalities which satisfy certain conditions.

• 충청수학회지
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• 제20권4호
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• pp.503-514
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• 2007

In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

• East Asian mathematical journal
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• 제36권1호
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• pp.35-53
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

• 대한수학회논문집
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• 제28권4호
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• pp.767-782
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• 2013

We deal with the Hyers-Ulam stability problem of linear mappings from a vector space into a Banach one with respect to the following functional equation: $$f\(\frac{-x+y}{3}\)+f\(\frac{x-3z}{3}\)+f\(\frac{3x-y+3z}{3}\)=f(x)$$. We then combine this equation with other ones and establish the Hyers-Ulam stability of several kinds of linear mappings, among which the algebra (*-) homomorphisms, the derivations, the multipliers and others. We thus repair and improve some previous assertions in the literature.

• 호남수학학술지
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• 제42권2호
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• 대한수학회논문집
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• 제39권3호
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• pp.673-692
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• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• 대한수학회보
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• 제46권2호
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• pp.387-400
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• 2009

We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.

• 충청수학회지
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• 제21권1호
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• pp.1-14
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• 2008

In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated 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.