Asymptotic properties of isometries

AbstractIn this paper, we prove two theorems on the local stability of isometries in connection with (ε,p)-isometries. These theorems reveal that a large class of (ε,p)-isometries, defined on various restricted domains, are stable

On the Stability of a Multiplicative Functional Equation

AbstractIn this paper, we will introduce a new multiplicative functional Eq. (1) and prove that the given equation is equivalent to the well known “original” one, f(xy)=f(x)f(y). Moreover, we will investigate the stability problem of Eq. (1) in the sense of R. Ger

On the Hyers–Ulam–Rassias Stability of a Quadratic Functional Equation

AbstractIn this paper, we investigate the Hyers–Ulam–Rassias stability problems of a new quadratic functional equationfx−y−z+fx+fy+fz=fx−y+fy+z+fz−x.Furthermore, the stability results will be applied to the study of an interesting asymptotic property of the quadratic functions

Bessel's Differential Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation

A Note on Stability of an Operator Linear Equation of the Second Order

We prove some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers). In this way, we obtain several results on stability of some linear functional and differential and integral equations of the second order and some fixed point results for a particular (not necessarily linear) operator