INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES

Nisar Ahmad Rather     (University of Kashmir, Hazratbal, Srinagar, Jammu and Kashmir 190006, India)
Mohmmad Shafi Wani     (University of Kashmir, Hazratbal, Srinagar, Jammu and Kashmir 190006, India)
Ishfaq Dar     (Institute of Technology, Zakura Campus, University of Kashmir, Srinagar, India)

Abstract


Let \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of 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 set up some results for rational functions with fixed poles and restricted zeros. The obtained results bring forth generalizations and refinements of some known inequalities for rational functions and in turn produce generalizations and refinements of some polynomial inequalities as well.

Keywords


Rational functions, Polynomials, Inequalities

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References


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DOI: http://dx.doi.org/10.15826/umj.2022.2.012

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