Inequalities for a class of rational functions

In this paper, we consider a more general class of rational functions r(s(z)), of degree mn, with s(z) being a polynomial of degree m. Our results not only generalize the results due to Wali and Shah [JOA, \textbf{25} (2017), no. 1, 43-53] but also improve the results obtained by Qasim and Liman [Indian. J. Pure Appl. Math. \textbf{46} (2015), no. 3, 337-348] and Mir [Indian J. Pure Appl. Math. \textbf{50} (2019), no. 2, 315-331].