On a type of exponential functional equation and its superstability in the sense of Ger

In this paper, we deal with a type exponential functional equation as follows $$f(xy)=f(x)^{g(y)},$$ where $f$ and $g$ are two real valued functions on a commutative semigroup. Our aim of this paper is to proved that the above functional equation in the sense of Ger is superstable

Finsler Metrics with Bounded Cartan Torsions

The norm of Cartan torsion plays an important role for studying of immersion theory in Finsler geometry. Indeed, Finsler manifold with unbounded Cartan torsion can not be isometrically imbedded into any Minkowski space. In this paper, we find two subclasses of (?, ?)-metrics which have bounded Cartan torsion. Then, we give two subclasses of (?, ?)-metrics whose bound on the Cartan torsions are independent of the norm of ?