• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.557-564
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• 2010

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.587-600
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• 2016

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

• Korean Journal of Mathematics
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• 제19권1호
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• pp.33-52
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• 2011

We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.

• 대한수학회보
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• 제39권3호
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• pp.401-410
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

• 대한수학회보
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• 제45권1호
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• pp.133-142
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• 2008

Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.

• 대한수학회논문집
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• 제28권2호
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• 대한수학회보
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• 제41권2호
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• pp.347-357
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• 2004

In this note we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the cubic functional equation f(3$\chi$+y) + f($3\chi$-y) = $3f(\chi$+ y) + $3f(\chi$-y) + ($48f(\chi)$ on abelian groups.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.205-214
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• 2008

In this paper, we prove the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation $2f(x+y,\frac{z+w}{2})=f(x,z)+f(x,w)+f(y,z)+f(y,w)$ in the spirit of $P.G{\breve{a}}vruta$.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.343-361
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.