On Eneström-Kakeya theorem for a quaternionic polynomial

• Autorzy: Mogbademu Adesanmi A.

Identyfikatory

DOI

10.21008/j.0044-4413.2023.0007

• Języki publikacji: EN

Abstrakty

EN

Let p(q) = ∑ⁿ_l=0 q^l a_l be a quaternion polynomial of degree n with quaternion coefficients a and quaternion variable q, where a_l = α_l + iβ_l + jγ_l + kδ_l for 0 ≤ l ≤ n. In this paper, we put some restrictions on the coefficients of p(q) to obtain some new Eneström-Kakeya’s Theorems for a polynomial with quaternion variable.

Słowa kluczowe

EN

Eneström-Kakeya theorem; zeros of polynomials; quaternions

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2023
• Tom: nr 66
• Strony: 81--90
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Mogbademu Adesanmi A.

• Department of Mathematics, University of Lagos, Lagos Nigeria

Bibliografia

• [1] Carney N., Gardner R., Keaton R., Powers A., The Eneström-Kakeya theorem for polynomials of a quaternionic variable, J. Approx. Theor., 250(2020), 105325: https://doi.org/10.1016/j.jat.2019.105325.
• [2] Cauchy A.L., Exercise de Mathematique, Oeuvres, 2(9) (1829), 122.
• [3] Dewan K.K., Govil N.K., On the Eneström-kakeya theorem, J. Approx. Theory, 42(1984), 239-244.
• [4] Dewan K.K., Govil N.K., On the Eneström-kakeya theorem, J. Math. Anal. Appl., 180(1993), 29-36.
• [5] Gardener R.G., Govil N.K., Some generalizations of the Eneström-Kakeya theorem, Acta Math. Hungar, 4(1997), 125-134.
• [6] Gauss K.F., Beitrage zur Theorie der algebraischen Gleichungen, Abh. Ges. Wiss. Gottingen, 4 (1850), 73-102.
• [7] Gentili G., Stoppato C., Zeros of regular functions and polynomials of a quaternionic variable, Michigan Math. J., 56(2008), 655-667.
• [8] Gentili G., Struppa D., A new theory of regular functions of a quaternionic variable, Adv. Math., 216(2007), 279-301.
• [9] Joyal A., Labelle G., Rahman Q.I., On the Location of Zeros of Polynomials, Canadian Math. Bull., 10(1967), 55-63.
• [10] Karam J.R., An application of the Kakeya-Eneström theorem, Proc. Int. Conf. Image Sci. in Syst. Technol. CISST, 04(2004), 354-358.
• [11] Marden M., Geometry of polynomials, Math. Surveys, No. 3, Amer. Math. Soc. Providence, RI (1949).
• [12] Milovanovic G.V., Mitrinovic D.S., Rassias Th.M., Topics in Polynomials: extremal properties, inequalities, zeros, World Scientific Publishing Co., Singapore, 1994.
• [13] Pogorui P., Shapiro M., On the structure of the set of zeros of quaternionic polynomials, Complex Var. Elliptic Equ., 49(2004), 379-389.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).