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Fuzzy differential subordinations connected with the linear operator

Sheza M. El-Deeb, Georgia I. Oros (2021)

Mathematica Bohemica

We obtain several fuzzy differential subordinations by using a linear operator m , γ n , α f ( z ) = z + k = 2 ( 1 + γ ( k - 1 ) ) n m α ( m + k ) - α a k z k . Using the linear operator m , γ n , α , we also introduce a class of univalent analytic functions for which we give some properties.

Generalization of a Conjecture in the Geometry of Polynomials

Sendov, Bl. (2002)

Serdica Mathematical Journal

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros...

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

Iliev, Anton (1998)

Serdica Mathematical Journal

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

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