Fixed points and fuzzy stability of an additive-quadratic functional equation
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation
On Hilbert Golab-Schinzel type functional equation
Let X be a vector space over a field K of real or complex numbers. We will prove the superstability of the following Go lab-Schinzel type equation f(x+ g(x)y) = f(x)f(y), x, y 2 X, where f, g : X ! K are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Our result refers to papers by Chudziak and Tabor (J. Math. Anal. Appl. 302 (2005) 196-200), Jab lonska (Bull. Aust. Math. Soc. 87 (2013), 10-17) and Rezaei (Math. Ineq. Appl., 17 (2014), 249-258).
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.