• 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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• 제33권1_2호
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• pp.45-60
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• 2015

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

• 충청수학회지
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• 제30권4호
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• pp.467-476
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• 2017

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.

• 충청수학회지
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• 제14권2호
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• pp.37-46
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• 2001

In this paper, weighted Bloch spaces $\mathcal{B}_q$ are considered on the open unit ball in $\mathbb{C}^n$. In this paper, we will show that every Bloch function in $B_q$ induces a bounded linear functional on $L^1_a(\mathcal{B})$.

• East Asian mathematical journal
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• 제30권3호
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• pp.271-281
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• 2014

In this paper, we consider the following cubic functional equation f(3x + y) + f(3x - y) = f(x + 2y) + 2f(x - y) + 2f(3x) - 3f(x) - 6f(y) and prove the generalized Hyers-Ulam stability for it in fuzzy normed spaces.

• 대한수학회논문집
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• 제26권2호
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• pp.237-251
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• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• 대한수학회논문집
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• 제25권3호
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• pp.405-417
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• 2010

We prove the generalized Hyers-Ulam stability of the generalized quadratic functional equation $$f(rx\;+\;sy)\;=\;r^2f(x)\;+\;s^2f(y)\;+\;\frac{rs}{2}[f(x\;+\;y)\;-\;f(x\;-\;y)]$$ in fuzzy Banach spaces, where r, s are non-zero rational numbers with $r^2\;+\;s^2\;{\neq}\;1$.

• 충청수학회지
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• 제34권4호
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.85-92
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• 2024

In this work we give the necessary and sufficient conditions for f-biharmonic curves in three-dimensional generalized symmetric spaces.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.83-90
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• 2005

A.H.Hamel proved the Ekeland's principle in a locally convex Hausdorff topological vector spaces by constructing the norm and applying the Ekeland's principle in Banach spaces. In this paper we show that the Ekeland's principle in a locally convex Hausdorff topological vector spaces can be proved directly by applying the famous general principle of H.Br$\acute{e}$zis and F.E.Browder.