• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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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.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.371-380
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• 2002

In this paper we obtain the general solution of a quadratic Jensen type functional equation : (equation omitted) and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.559-569
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• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.283-295
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• 2002

In this Paper we show the Solution of the following Jensen functional equation with three variables and prove the stability of this equations in the spirit of Hyers, Ulam, Rassias and Gavruta: (equation omitted).

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.231-247
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• 2010

In this paper, we investigate the generalized Hyers-Ulam stability of a 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). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.73-81
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• 2015

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.635-645
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• 2015

We will show the general solution of the functional equation $$\begin{eqnarray}f(x+ay)+f(x-ay)+2(a^2-1)f(x)\\=a^2f(x+y)+a^2f(x-y)+2a^2(a^2-1)f(y)\end{eqnarray}$$ and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.345-350
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• 2013

Some results on the sensitivity of the solution of the generalized Lyapunov equation $$A^{n-1}X+A^{n-2}XA^*+{\cdots}+X(A^*)^{n-1}=B$$ are shown follow easily from well-known theorems in functional analysis.