This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Num...

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

A familiar functional equation f(ax+b) = cf(x) will be solved in the class of functions f : R → R. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f ( a1x1+···+amxm+x0 )= m ∑ i=1 bif ( ai1x1+···+aimxm ) in connection with the question of Rassias and Tabor.