arXiv subjects
Publications and source records attributed to M. Alimohammady.
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.
Our aim of this paper is to study a family of functional equation in vector and Banach spaces with difference operators, where this family of functional equation is a general mixed additive-quadratic-cubic-quartic functional equations. We show that every function satisfies the our functional equation is a monomial function with a certain degree. Furthermore, we deal with the generalized Hyers-Ulam stability of this family of functional equations in Banach space.
In this paper, we show that D-compactness in Generalized Šerstnev spaces implies D-boundedness and as in the classical case, a D-bounded and closed subset of a characteristic Generalized Šerstnev is not D-compact in general. Finally, in the finite dimensional Generalized Šerstnev spaces a subset is D-compact if and only if is D-bounded and closed.