Let P(z) be a polynomial of degree n having all its zeros in \(|z|\le k,~k\ge 1,\) it is known for every non-zero vector \(\gamma =(\gamma _1,\gamma _2,\ldots ,\gamma _n), ~\gamma _j\ge 0, ~1\le j\le n,\) that 1 \(\begin{aligned} \max _{|z|=1}|D_\alpha ^\gamma P(z)|\ge \frac{|\gamma |}{1+k^n}(|\alpha |-k)\max _{|z|=1}|P(z)|, \end{aligned}\) where \(D_\alpha ^\gamma P(z)\) is the generalized polar derivative of P(z) with respect to a real or complex number \(\alpha \) and \(|\gamma |=\sum _{j=1}^{n}\gamma _j\) . In this paper, we shall present the \(q-\) integral mean extension of (1). The results obtained not only provide a parallel analogue of inequalities for the polar derivative of a polynomial but also yield other interesting inequalities as special cases.
