On the weakened hypotheses-based generalizations of the Enestr\"{o}m-Kakeya theorem
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According to the well-known Enestr\"{o}m-Kakeya Theorem, all the zeros of a polynomial $P(z)=\sum\limits_{s=0}^{n}a_sz^s$ of degree $n$ with real coefficients satisfying $a_n\geq a_{n-1}\geq\cdots\geq a_1\geq a_0>0$ lie in the complex plane $|z|\leq1.$ We provide comparable results with hypotheses relating to the real and imaginary parts of the coefficients as well as the coefficients' moduli in response to recent findings about an Enestr\"{o}m-Kakeya ``type" condition on real coefficients. Our findings so broadly extend the other previous findings.
Abstract
According to the well-known Enestr\"{o}m-Kakeya Theorem, all the zeros of a polynomial $P(z)=\sum\limits_{s=0}^{n}a_sz^s$ of degree $n$ with real coefficients satisfying $a_n\geq a_{n-1}\geq\cdots\geq a_1\geq a_0>0$ lie in the complex plane $|z|\leq1.$ We provide comparable results with hypotheses relating to the real and imaginary parts of the coefficients as well as the coefficients' moduli in response to recent findings about an Enestr\"{o}m-Kakeya ``type" condition on real coefficients. Our findings so broadly extend the other previous findings.
참고문헌 (10)
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