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

Unit-sphere preserving mappings

We prove that if a one-to-one mapping f : (n ≥ 2) preserves the unit n - 1 spheres (Sn -1), then f is a linear isometry up to translation

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