The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations \[ x_{n+1}=\frac{x_{n-14}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}},\ \ \ \ n=0,1,2,\ldots,\] where the initial conditions \(x_{-14},x_{-13},\ldots,x_{0}\) are arbitrary real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. Finally, we confirm the results with some numerical examples and graphs by using Matlab program.

In this paper, we will prove some new weighted Čebyšev-Ostrowski type inequalities with power mean on time scales. The results will be proved by employing the generalized version of Montgomery's identity with weights that will be proved for our purpose. As special cases, we will derive some new weighted discrete inequalities of Čebyšev-Ostrowski type which to the best of the authors' knowledge are essentially new.