325 citations · 362 across the 22 of their papers we have counts for
24 papers · 1 filter
On the extension of analytic solutions of first-order difference equations
Rod Halburd, Risto Korhonen, Yan Liu +1
We will consider first-order difference equations of the form \[ y(z+1) = \frac{λy(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $λ\in\mathbb{C…
Zero order meromorphic solutions of -difference equations of Malmquist type
Risto Korhonen, Yueyang Zhang
We consider the first order -difference equation \begin{equation}\tag† f(qz)^n=R(z,f), \end{equation} where is a constant and is rational in both arguments.…
A new proximity function estimate on the quotient of the difference and the derivative of a meromorphic function
Lasse Asikainen, Juha-Matti Huusko, Risto Korhonen
It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function , \begin{equation*} m\left(r,\frac{Δ_cf - ac}{f' - a}\right)=S(r,f'…
On meromorphic solutions of Malmquist type difference equations
Yueyang Zhang, Risto Korhonen
Recently, the present authors used Nevanlinna theory to provide a classification for the Malmquist type difference equations of the form that have transcend…
A Malmquist--Steinmetz theorem for difference equations
Yueyang Zhang, Risto Korhonen
It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where is rational in both arguments and , has a transcendental merom…
Studies of Differences from the point of view of Nevanlinna Theory
Jianhua Zheng, Risto Korhonen
This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic f…