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Displaying similar documents to “Inequalities for entire functions of finite degree and for polynomials.”

The generalized Laguerre inequalities and functions in the Laguerre-Pólya class

George Csordas, Anna Vishnyakova (2013)

Open Mathematics

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The principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and...

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. Dewan, Sunil Hans (2011)

Annales UMCS, Mathematica

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In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.