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Some extensions of Enestrom-Kakeya theorem for quaternionic polynomials
Shahbaz Mir,Abdul Liman 강원경기수학회 2022 한국수학논문집 Vol.30 No.4
In this paper, we will prove some extensions of the Enestr\"{o}m-Kakeya theorem to quaternionic polynomials which were already valid for the classical Enestr\"{o}m-Kakeya theorem to complex polynomials. Our kind of extensions have considerably improved the bounds by relaxing and weakening the hypothesis in some cases.
On the number of zeros of bicomplex entire functions
Shahbaz Mir,Abdul Liman 강원경기수학회 2023 한국수학논문집 Vol.31 No.3
This paper portrays the results on bicomplex entire functions that are concerned with the positioning of zeros of Eneström-Kakeya type. Moreover, some examples are provided to validate our results.
On the weakened hypotheses-based generalizations of the Enestr\"{o}m-Kakeya theorem
Shahbaz Mir,Abdul Liman 강원경기수학회 2024 한국수학논문집 Vol.32 No.2
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.