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On the maximum modulus of a polynomial

Jain Vinay Kumar

Journal of Mathematics and Applications

2019

Vol. 42

109--116

For a polynomial p(z) of degree n, having no zeros in |z| < 1 Ankeny and Rivlin had shown that for R ≥ 1 [wzór]. Using Govil, Rahman and Schmeisser’s refinement of the generalization of Schwarz’s lemma we have obtained a refinement of Ankeny and Rivlin’s result. Our refinement is also a refinement of Dewan and Pukhta’s refinement of Ankeny and Rivlin’s result.

A refinement of Schwarz's lemma and its applications

Jain V. K.

Journal of Mathematics and Applications

2016

Vol. 39

69--80

By using the value of the second derivative of the function at 0, along with the values of the function and its first derivative at 0, we have obtained a refinement of well known Schwarz’s lemma and have used this refinement to obtain refinements, of Aziz and Rather’s inequalities [2004] for a polynomial of degree n having no zeros in |z| < k, (k ≥ 1).

Growth theorems for 4-quasihomographies of the real line

Szynal A.

Journal of Mathematics and Applications

2007

Vol. 29

137-141

In this paper we present growth theorems for 4-quasihomographies of the real line.

Univalence criterion for certain integral operators

Hamada H.

Demonstratio Mathematica

2005

Vol. 38, nr 1

43--46

Pescar investigated the univalence of certain integral operators. We will show that the results are obtained by the Schwarz lemma. We will also give some generalizations.

An elementary proof a Schwarz lemma for the symmetrized bidisc

Hamada H, Segawa H.

Demonstratio Mathematica

2003

Vol. 36, nr 2

329--334

Agler-Young obtained a Schwarz lemma for the symmetrized bidisc. Their proof uses an earlier result of them whose proof is operator-theoretic in nature. They posed the question to give an elementary proof of the Schwarz lemma for the symmetrized bidisc. In this paper, we give an elementary proof of the Schwarz lemma for the symmetrized bidisc.

Quasihomographies of the real line

Szynal Anetta

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

155-164

In this paper we present some properties of normalized (fixed in points x1, x2, infinity k-quasihomographies of the real line.