# Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros

## Related Articles

- Real zeros of some classes of analytic functions determined by a majorant of infinite order. Shamoyan, F. // Journal of Mathematical Sciences;Jan2011, Vol. 172 Issue 2, p276
Certain classes of entire functions or of functions analytic in the unit disk are treated; they are defined in terms of a radial majorant ? that grows sufficiently fast. Under certain assumptions on ?, we describe the zero sets for such a class that lie on R (respectively, on the segment [0,...

- On Bounds For The Zeros of Univariate Polynomials. Dehmer, Matthias; Kilian, J�rgen // Proceedings of World Academy of Science: Engineering & Technolog;2007, Vol. 20, p205
Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we...

- Inequalities for the Polar Derivative of a Polynomial. Bidkham, M.; Shakeri, M.; Gordji, M. Eshaghi // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1
Let p(z) be a polynomial of degree n and for any real or complex number Î±, and let DÎ±p(z) = np(z) + (Î± - z)p'(z) denote the polar derivative of the polynomial p(z) with respect to Î±. In this paper, we obtain new results concerning the maximum modulus of a polar derivative of a...

- Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function. Saker, Samir H. // Journal of Inequalities & Applications;2010, Vol. 2010, p1
On the hypothesis that the (2k)th moments of the Hardy Z-function are correctly predicted by random matrix theory and the moments of the derivative of Z are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the...

- THE CONVERGENCE OF DURAND-KERNER METHOD FOR SIMULTANEOUSLY FINDING ALL ZEROS OF THE POLYNOMIAL. Dan-fu Han // Journal of Computational Mathematics;Nov2000, Vol. 18 Issue 6, p567
In this paper we propose the two kinds of different criterions and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods.

- Questions About Polynomials with (0, -1, + 1) Coefficients: Research Problems 96-3. Borwein, P.; Erdélyi, T. // Constructive Approximation;1996, Vol. 12 Issue 3, p439
Presents questions about polynomials concerning the location and multiplicity of zeros of polynomials with smaller integer coefficients.

- On the location of zeros of polynomials and related analytic functions. Aziz, Abdul; Shah, W.M. // Nonlinear Studies;1999, Vol. 6 Issue 1, p91
Provides information on a study which proved a more general result concerning the location of zeros of a polynomial. Statements of results; Theorems and proofs.

- Certain generalizations of EnestrÃ¶m-Kakeya theorem. Singh, Gulshan; Shah, W.M. // Journal of Advanced Research in Applied Mathematics;2012, Vol. 4 Issue 2, p16
In this paper, we prove some generalizations of results concerning the EnestrÃ¶m-Kakeya theorem. The results obtained considerably improve the bounds by relaxing the hypothesis in some cases.

- Approximation to the function z by rational fractions in a domain with zero external angle. Pekarskii, A. // Mathematical Notes;May2012, Vol. 91 Issue 5/6, p714
Rational approximations to the function z, Î± âˆˆ â„ \ â„¤, were studied by Newman, Gonchar, Bulanov, Vyacheslavov, Andersson, Stahl, and others. The present paper deals with the order of best rational approximations to this function in a domain with zero external angle and vertex...