INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES

Let \(\Re_n\) be the set of all rational functions type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial degree at most \(n\) and \(w(z) \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we up some results with fixed poles restricted zeros. The obtained bring forth generalizations refinements known inequalities in turn produce as well.