Quaternionic Generalization of the Enestr\"om-Kakeya Theorem

Key Points

• All zeros of the quaternionic polynomial lie within the unit ball, confirming the generalization of a classical theorem.
• The polynomial considered has non-negative, monotonically increasing coefficients, setting strict conditions on its zeros.
• This analysis builds upon previous generalizations of the Eneström-Kakeya Theorem in the literature, demonstrating significant mathematical extensions.
• The findings could influence future research in polynomial theory and quaternionic algebra, offering new avenues for exploration.