A note on Enstr\"{o}m-Kakeya theorem for quaternionic polynomials
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In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. We derive new bounds of Enestr\"{o}m-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.
Abstract
In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. We derive new bounds of Enestr\"{o}m-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.
참고문헌 (11)
- A. Aziz, "Some extension of Enestr¨om-Kakeya theorem", Glas´nik Mathematiki, 31, pp.239~244 (1996)
- N. Carney, "The Enestr¨om-Kakeya theorem of a quaternionic variable", J. Approx. Theory, 250, pp.105~325 (2020)
- A. Cauchy, "Exercises de math´ematique", Oeuvres, 9, pp.122~ (1829)
- G. Enestr¨om, "Remarque sur un th´eor´eme relatif aux racines de I’´equation anx n +. . . + a0 = 0o´u tous les coefficients sont r´eels et positifs", Tˆohoku Math. J, 18, pp.34~36 (1920)
- G. Gentili, "Zeros of regular functions and polynomials of a quaternionic variable", Michigan Math. J, 56, pp.655~667 (2008)
- G. Gentili, "A new theory of regular functions of a quaternionic variable", Adv. Math, 216, pp.279~301 (2007)
- N. K. Govil, "On the Enestr¨om-Kakeya theorem", Tˆohoku Math. J, 20, pp.126~136 (1920)
- A. Joyal, "On the location of zeros of polynomials", Can. Math. Bull, 10, pp.53~63 (1967)
- M. Marden, "Geometry of polynomials", Math. Surveys, 3 (1966)
- G. V. Milovanovi´c, "Topics in polynomials: Extremal problems, Inequalities, Zeros" (1994), World Scientific publishing Co
- D. Tripathi, "A note on Enestr¨om-Kakeya theorem for a polynomial with quaternionic variable", Arab. J. Math, 9, pp.707~714 (2020)