On a functional equation related to a generalization of Flett's mean value theorem.
Generating solutions of some Cauchy and cosine functional equations.
On extending functions to solutions of some functional equations.
The continuous solution of a functional equation of Abel.
On extending functions to solutions of some functional equations. (Short Communications).
The law of large numbers and a functional equation
We deal with the linear functional equation (E) , where g:(0,∞) → (0,∞) is unknown, is a probability distribution, and ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
On the uniqueness of continuous solutions of a functional equation of n-th order.
Errata list for "Mean values for vector valued functions and corresponding functional equations" (Commentationes Mathematicae 53(2) (2013), 355-369)
Mean values for vector valued functions and corresponding functional equations
Although, in general, a straightforward generalization of the Lagrange mean value theorem for vector valued mappings fails to hold we will look for what can be salvaged in that situation. In particular, we deal with Sanderson’s and McLeod’s type results of that kind (see [9] and [7], respectively). Moreover, we examine mappings with a prescribed intermediate point in the spirit of the celebrated Aczél’s theorem characterizing polynomials of degree at most 2 (cf. [1]).
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