• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권3호
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• pp.185-192
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• 2003

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

• 충청수학회지
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• 제35권2호
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• pp.149-159
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• 2022

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

• 대한수학회보
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• 제31권1호
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• pp.45-54
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• 1994

Throughout this paper, the definitions and properities related to probabilistic normed spaces are followed as in [2]. Let R be the set of all real numbers. A mapping F:R .rarw. [0, 1] is called a distribution function on R if it is nondecreasing and left continuous with inf F = 0 and sup F = 1. We denote by L the set of all distribution functions on R.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.359-367
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• 2009

The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

• 대한수학회논문집
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• 제38권2호
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• pp.509-524
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• 2023

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and Găvruţa stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-𝛽-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

• 대한수학회보
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• 제13권2호
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• pp.127-135
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• 1976

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권2호
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.435-445
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• 2015

In this paper, using the fixed point method, we investigate the generalized Hyers-Ulam stability of the system of quintic functional equation $f(x_1+x_2,y)+f(x_1-x_2,y)=2f(x_1,y)+2f(x_2,y)\;f(x,2_{y1}+y_2)+f(x,2_{y1}-y_2)=f(x,y_1-2_{y2})+f(x,y_1+y_2)\;-f(x,y_1-y_2)+15f(x,y_1)+6f(x,y_2)$ in non-Archimedean 2-Banach spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.573-581
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• 1997

In this paper we prove a weak common fixed point theo-rem in a normed almost linear space which is different from the result of S. P. Singh and B.A. Meade [9]. However for a Banach X our theorem is equal to the result of S. P. Singh and B. A. Meade.