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

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

Hyers-Ulam stability of a generalized Hosszu functional equation

In this paper, we investigate the Hyers-Ulam stability of a generalized Hosszu functional equation, namely f(x + y - xy ) + g(xy) = h(x) + k(y), where f, g, h, k are functions of a real variable with values in a Banach space

On the Stability of One-Dimensional Wave Equation

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, utt=c2uxx, in a class of twice continuously differentiable functions

On the Stability of Wave Equation

We prove the generalized Hyers-Ulam stability of the wave equation, Δu=(1/c2)utt, in a class of twice continuously differentiable functions under some conditions