• 충청수학회지
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• 제22권4호
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• pp.815-830
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• 2009

In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

• 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.

• 대한수학회보
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• 제60권3호
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• pp.717-732
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• 2023

The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ²ⁿ⁺¹(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4) × ℝ.

• 대한수학회보
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• 제50권6호
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• pp.2061-2070
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• 2013

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.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1177-1194
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• 2009

In this paper we establish the general solution of the functional equation f(2x+y)+f(x-2y)=2f(x+y)+2f(x-y)+f(-x)+f(-y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from 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.

• 대한수학회보
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• 제47권4호
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• pp.777-785
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• 2010

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\rightarrow$ Y, which satisfies the inequality ${\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)$ for suitable control function $\varphi$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $t\;{\mapsto}\;f(tx)$ and $t\;{\mapsto}\;\varphi(tx,\;ty)$ imply the continuity of $t\;{\mapsto}\;M(tx)$.

• 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.

• 충청수학회지
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• 제26권1호
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• pp.221-229
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• 2013

We show that if X is a space such that ${\beta}QF(X)=QF({\beta}X)$ and each stable $Z(X)^{\sharp}$-ultrafilter has the countable intersection property, then there is a homeomorphism $h_X:vQF(X){\rightarrow}QF(vX)$ with $r_X={\Phi}_{vX}{\circ}h_X$. Moreover, if ${\beta}QF(X)=QF({\beta}X)$ and $vE(X)=E(vX)$ or $v{\Lambda}(X)={\Lambda}(vX)$, then $vQF(X)=QF(vX)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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• pp.103-108
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• 2013

Observing that for any space X, there is a Wallman sublattice $\mathfrak{A}_X$ and that QFX is homeomorphic to a subspace $X_q$ of the Wallman cover $\mathfrak{L}(\mathfrak{A}_X)$ of $\mathfrak{A}_X$, we show that ${\beta}QFX$ and $\mathfrak{L}(\mathfrak{A}_X)$ are homeomorphic.

• 충청수학회지
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• 제26권4호
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• pp.757-767
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• 2013

We investigate the general solution of the following functional equation and the generalized Hyers-Ulam-Rassias stability problem in quasi ${\beta}$-normed spaces and then the stability by using alternative fixed point method for the following quintic function $f:X{\rightarrow}Y$ such that f(3x+y)+f(3x-y)+5[f(x+y)+f(x-y)]=4[f(2x+y)+f(2x-y)]+2f(3x)-246f(x), for all $x,y{\in}X$.