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On Eneström-Kakeya theorem for a quaternionic polynomial

100%

Mogbademu A. A.

Fasciculi Mathematici

2023

tom nr 66

81--90

Let p(q) = ∑nl=0 ql al be a quaternion polynomial of degree n with quaternion coefficients a and quaternion variable q, where al = αl + iβl + jγl + kδl 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.

On the number of zeros of a polynomial in a region

100%

Kareem K. A. , Mogbademu A. A.

Fasciculi Mathematici

2016

tom Nr 57

53--65

In this paper, we impose restrictions on the complex coefficients of a polynomial in order to give bounds concerning the number of zeros in a specific region of the complex plane. Our results generalize and refine a good number of results in this area of research.

On circularly symmetric functions

88%

Koczan L. , Zaprawa P.

Journal of Mathematics and Applications

2014

tom Vol. 37

59--66

[...] In this paper besides X we also consider some of its subclasses: X(...) and Y (...) S consisting of functions in X with the second coeffcient fixed and univalent starlike functions respectively. According to the suggestion, in Abstract we add one more paragraph at the end of the section: For X(...) we find the radii of starlikeness, starlikeness of order (alfa), univalence and local univalence. We also obtain some distortion results. For Y (...) S we discuss some coecient problems, among others the Fekete-Szego ineqalities.

Pentadiagonal Companion Matrices

75%

Eastman B. , Vander Meulen K. N.

Special Matrices

2016

tom 4

nr 1

13-30

The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find a Fiedler factorization, up to transpose, given only its corner entries.