• 충청수학회지
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• 제31권4호
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• pp.397-409
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• 2018

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation $$f\({\sum\limits_{i=1}^{n}}x_i\)+{\sum\limits_{1{\leq}i<j{\leq}n}}f(x_i-x_j)-n{\sum\limits_{i=1}^{n}f(x_i)=0$$ for integer values of n such that $n{\geq}2$, where f is a mapping from a vector space V to a Banach space Y.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.423-430
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• 2003

We prove the generalized Hyers-Ulam-Rhssias stability of the Jensen's equation in Banach modules over a Banach algebra.

• 충청수학회지
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• 제33권1호
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• pp.9-18
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• 2020

In this paper, we investigate the stability of a quadratic-cubic-quartic functional equation $$f(x+ky)+f(x-ky)-k^2f(x+y)-k^2f(x-y)-2(1-k^2)f(x)-{\frac{k^2(k^2-1)}{6}}(f(2y)+2f(-y)-6f(y))=0$$ by applying the direct method in the sense of Gǎvruta.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.171-180
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• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.

• 대한수학회보
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• 제49권2호
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• pp.339-352
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• 2012

We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).

• 충청수학회지
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• 제15권1호
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• pp.53-60
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• 2002

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of linear operators in Banach modules over a unital $C^*$-algebra associated with its unitary group.

• 충청수학회지
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• 제29권1호
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• pp.103-108
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• 2016

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x_1+x_2)+f(x_2+x_3)+{\cdots}+f(x_n+x_1){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that $2{\leq}t$ < n.

• 충청수학회지
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• 제19권1호
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• pp.69-77
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• 2006

The generalized Hyers-Ulam stability problems of the mixed type functional equation $$f\({\sum_{i=1}^{4}xi\)+\sum_{1{\leq}i<j{\leq}4}f(x_i+x_j)=\sum_{i=1}^{4}f(x_i)+\sum_{1{\leq}i<j<k{\leq}4}f(x_i+X_j+x_k)$$ is treated under the approximately even(or odd) condition and the behavior of the quadratic mappings and the additive mappings is investigated.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.83-90
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• 2009

In this paper, we investigate isomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$$, which was introduced and investigated by Baak in [2].