120 citations · 295 across the 23 of their papers we have counts for
8 papers · 1 filter
On the Kurepa and inhomogeneous Cauchy functional equations
Rashid Aliev, Vugar Ismailov
It follows from de Bruijn's results that if a continuous or -th order continuously differentiable function is a solution of the Kurepa functional equation, then it can…
A note on the problem of straight-line interpolation by ridge functions
Azer Akhmedov, Vugar Ismailov
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of li…
The double difference property for the class of locally Hölder continuous functions
Rashid Aliev, Aysel Asgarova, Vugar Ismailov
In this paper, we show that the pair of classes of locally Hölder continuous functions (considered on and , respectively) has the double difference pro…
Notes on ridge functions and neural networks
Vugar Ismailov
These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They…
A representation problem for smooth sums of ridge functions
Rashid Aliev, Vugar Ismailov
In this paper we prove that if a multivariate function of a certain smoothness class is represented by a sum of arbitrarily behaved ridge functions, then it can be represented…
On the representation by bivariate ridge functions
Rashid Aliev, Vugar Ismailov
We consider the problem of representation of a bivariate function by sums of ridge functions. We show that if a function of a certain smoothness class is represented by a sum of fi…
On the proximinality of ridge functions
Vugar Ismailov
Using two results of Garkavi, Medvedev and Khavinson, we give sufficient conditions for proximinality of sums of two ridge functions with bounded and continuous summands in the spa…
On the approximation by weighted ridge functions
Vugar Ismailov
We characterize the best approximation to a multivariate function by linear combinations of ridge functions multiplied by some fixed weight functions. In the special case w…