Growth of solutions of some higher order linear difference equations

Abstract

This paper is devoted to studying the growth of solutions of equations of type $f(z+n)+\sum_{j=0}^{n-1}\{P_{j}(e^{z})+Q_{j}(e^{-z})\}f(z+j)=0$ and $f(z+n)+ \sum_{j=0}^{n-1}\{P_{j}(e^{A(z)})+Q_{j}(e^{-A(z)})\}f(z+j)=0$, where $P_{j}(z)$ and $Q_{j}(z)$ are polynomials in $z$ and $A(z)$ is a transcendental entire function. We prove three theorems of such type, which improve some results in [6,7].