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Some Coefficient Estimates for Polynomials on the Unit Interval

Qazi, M. A.Rahman, Q. I. — 2007

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05. In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.

Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem

M. A. Qazi — 2016

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In his work on F. Carlson's uniqueness theorem for entire functions of exponential type, Q. I. Rahman [5] was led to consider an infinite integral and needed to determine the rate at which the integrand had to go to zero for the integral to converge. He had an estimate for it which he was content with, although it was not the best that could be done. In the present paper we find a result about the behaviour of the integrand at infinity, which is essentially best possible. Stirling's formula for...

The Schwarz-Pick theorem and its applications

M. A. QaziQ. I. Rahman — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.

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