On a functional inequality arising in the construction of the product of several metric spaces.
In the present paper we give new formulas for a general solution of the linear difference equation of finite order with constant complex coefficients without necessity of solving the characteristic equation
The Shannon entropy has the sum form ∑f(pi) with f(x) = -x logx (x belonging to [0,1]). This together with the property of additivity leads to the 'sum' functional equation...
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line where is a fixed point of , with a possible exception for . The range of any non-constant continuous solution is an interval whose end-points are fixed by and which contains in its interior no fixed point except for . We also gave a characterization of the class of continuous...