Non-oscillation of a class of third order nonhomogeneous difference equations

Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of a class of linear third order non-homogeneous difference equations of the formy(n+3)+α(n)y(n+2)+β(n)y(n+1)+γ(n)y(n)=f(n),n⩾0,Δ3y(n-1)+a(n)Δ2y(n-1)+b(n)Δy(n)+c(n)y(n)=f(n-1),n⩾1andΔ(p(n-1)Δ2y(n-1))+q(n)Δy(n)+r(n)y(n)=f(n-1),n⩾1,where γ(n)≠0 and p(n)>0p(n)>0. The available methods, usually used for the study of difference equations, are developed appropriately for this purpose.