• 충청수학회지
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• 제29권2호
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• pp.287-328
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• 2016

In the current work, we define and find the general solution of the decic functional equation g(x + 5y) - 10g(x + 4y) + 45g(x + 3y) - 120g(x + 2y) + 210g(x + y) - 252g(x) + 210g(x - y) - 120g(x - 2y) + 45g(x - 3y) - 10g(x - 4y) + g(x - 5y) = 10!g(y) where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.

• 충청수학회지
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• 제13권1호
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• pp.79-85
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• 2000

In this paper, we have an affirmative solution of G. Godini's open question ([3]): If a normed almost linear space Y is complete, is the normed almost linear space B(X, (Y,C)) complete?

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권1호
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• pp.51-57
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• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.265-285
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• 2016

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.

• 대한수학회보
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• 제34권1호
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• pp.115-125
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• 1997

In [3,4,5], G. Godini introduced a normed almost linear space(nals), generalizing the concept of a normed linear space. In contrast with the case of a normed linear space, tha norm of a nals $(X, $\mid$$\mid$$\mid$ \cdot $\mid$$\mid$$\mid$)$ does not generate a metric on X $(for x \in X \backslash V_X we have $\mid$$\mid$$\mid$ x - x $\mid$$\mid$$\mid$ \neq 0)$.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• 한국콘텐츠학회논문지
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• 제2권4호
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• pp.99-103
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• 2002

본 논문에서는 t 준노름이 연속인 경우 이미 주어진 퍼지 측도에 관한 측정 가능한 함수의 준 노름 퍼지 적분을 이용하여 퍼지 측도를 정의하는 방법에 대해서 조사했다. 즉 (X, F, g)이 퍼지 측도 공간이라고 하고 h$\in$L$^\circ$(X), 이며 $\top$는 연속 t 준노름이라 하자. 그러면 임의의 $A\in$F에 대해 $\nu$(A)=$\int _A$h$\top$g에 의하여 정의된 집합치 함수 $\nu$는 (X, F)상에서 퍼지 측도이다.

• East Asian mathematical journal
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• 제24권2호
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• pp.169-176
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• 2008

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for noncompatible, discontinuous mappings without assuming completeness of the space. We also give an application of our theorem to best approximation theory.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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• pp.157-160
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• 2005

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

• 충청수학회지
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• 제13권1호
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• pp.71-78
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• 2000

The main goal of this paper is to prove the following theorem ; Let (X, ${\rho}_1$) be a fuzzy normed linear space over K and (Y, ${\rho}_2$) be a fuzzy Banach space over K. If ${\chi}_{B_{{\parallel}{\cdot}{\parallel}}}{\supseteq}{\rho}*$, then (CF(X,Y), ${\rho}*$) is a fuzzy Banach space, where ${\rho}*(f)={\vee}{\lbrace}{\theta}{\wedge}\frac{1}{t({\theta},f)}\;{\mid}\;{\theta}{\in}(0,1){\rbrace}$, $f{\in}CF(X,Y)$, $B_{{\parallel}{\cdot}{\parallel}}$ is the closed unit ball on (CF(X, Y), ${\parallel}{\cdot}{\parallel}$ and ${\parallel}f{\parallel}={\vee}{\lbrace}P^2_{{\alpha}^-}(f(x))\;{\mid}\;P^1_{{\alpha}^-}(x)=1,\;x{\in}X{\rbrace}$, $f{\in}CF(X,Y)$, ${\alpha}{\in}(0,1)$.