Generalization of Eneström-Kakeya theorem and its extension to analytic functions

Abstract

In this paper, by using standard techniques we shall obtain a result that gives regions containing all the zeros of a polynomial with real coefficients. Our result not only generalizes several well-known results concerning the location of zeros of polynomials but also yields an answer to a question raised by Professor N. K. Govil. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information about the bounds of zeros of polynomials than some known results. Mathematics subject classification (2010): 30A10, 30C15.