On the stability of the orthogonal Pexiderized Cauchy equation

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers-Ulam stability of the orthogonal Cauchy functional equation of Pexider type f₁(x+y)=f₂(x)+f₃(y), x⊥y in which ⊥ is the orthogonality in the sense of Rätz.     

Solution and stability of a cubic functional equation

In this paper, we investigate the general solution and the stability of a cubic functional equation f（x ＋ ny） ＋ f（x - ny） ＋ f（nx） = n^2 f（x ＋ y） ＋ n^2 f（x - y）＋ （n^3 - 2n^2 ＋ 2）f（x）,where n ≥ 2 is an integer. Furthermore, we prove the stability by the fixed point method.     

Exponential type functional equation and its Hyers-Ulam stability

We give the solution of the functional equation f(x+y)+λf(x)f(y)=Φ(x,y) under some conditions. Also we show its Hyers-Ulam stability.     

Construction of continuous solutions and stability for the polynomial-like iterative equation

Most of known results such as existence, uniqueness and stability for polynomial-like iterative equations were given under the assumption that the coefficient of the first order iteration term does not vanish. The existence with a non-zero leading coefficient was therefore raised as an open problem. It was positively answered for local C¹ solutions later. In this paper this problem is answered further by constructing C⁰ solutions. Moreover, we discuss the stability of those C⁰ solutions, which consequently implies a result of the stability for iterative roots.     

Zeros of solutions of certain second order linear differential equation

In this paper, we investigate the exponent of convergence of the zero-sequence of solutions of the differential equation

(1.3)     

A Fixed Point Approach to the Fuzzy Stability of a Mixed Typ e Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.     

Stability of a generalized quadratic functional equation in Schwartz distributions

We consider the Hyers-Ulam stability problem of the generalized quadratic functional equation
uoA＋voB-2woP1 - 2ko P2 =0,
which is a distributional version of the classical generalized quadratic functional equation
f（x＋y）＋g（x - y） - 2h（x） - 2k（y）=0     

On nonstability of the linear recurrence of order one

We show that, under some assumptions, the linear recurrence (or difference equation) of order one in a Banach space is nonstable in the Hyers-Ulam sense. Our results are also connected with the notion of shadowing in dynamical systems and computer sciences.     

On the stability of the linear differential equation of higher order with constant coefficients

We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki-Rassias sense. As a consequence we obtain the Hyers-Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established.     

On the Hyers-Ulam stability of the linear differential equation

We obtain some results on generalized Hyers-Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions.     

On the stability of a quartic functional equation

In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation

f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y).     

On approximation of approximate solutions of Dhombres' equation

Let f:S→X map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability of Dhombres' equation

     

具偏差变元高阶Lienard方程周期解存在性

利用重合度理论,研究了一类具偏差变元高阶L ienard型方程周期解的存在性,获得了该方程至少存在一个周期解的充分条件.     

Asymptotic aspect of the quadratic functional equation in multi-normed spaces

We investigate the Hyers-Ulam stability of the quadratic functional equation for mappings from abelian groups into multi-normed spaces. We also study the stability on a restricted domain and present an asymptotic behavior of the quadratic equation in the framework of multi-normed spaces.     

Hyers-Ulam stability of linear differential equations of first order, III

Let X be a complex Banach space and let I=(a,b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty^′(t)+αy(t)+βtrx₀=0 for the class of continuously differentiable functions , where α, β and r are complex constants and x₀ is an element of X. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.     

具无穷时滞高阶中立型微分方程的周期解

利用重合度理论研究了一类具有无穷时滞高阶中立型泛函微分方程周期解的存在性,获得了该方程存在周期解的充分条件,推广和改进了二阶方程的相应结果.     

Orthogonality and quintic functional equations

Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.     

Analytic solutions of a second order iterative functional differential equation

This paper is concerned with an iterative functional differential equation

c₁x(z)+c₂x^′(z)+c₃x^″(z)=x(az+bx^′(z))