410 research outputs found
Integral mean estimates for the polar derivative of a polynomial
Let be a polynomial of degree having all zeros in
where then it was proved by Dewan \textit{et al} that for every real
or complex number with and each
\indent In this paper, we shall present a refinement and generalization of
above result and also extend it to the class of polynomials
having
all its zeros in where and thereby obtain certain
generalizations of above and many other known results.Comment: 8 page
New Generalizations of Exponential Distribution with Applications
The main purpose of this paper is to present k-Generalized Exponential Distribution which among other things includes Generalized Exponential and Weibull Distributions as special cases. Besides, we also obtain three-parameter extension of Generalized Exponential Distribution. We shall also discuss moment generating functions (MGFs) of these newly introduced distributions
Lp mean estimates for an operator preserving inequalities between polynomials
If be a polynomial of degree at most which does not vanish in , it was recently formulated by Shah and Liman \cite[\textit{Integral
estimates for the family of -operators, Operators and Matrices,}
\textbf{5}(2011), 79 - 87]{wl} that for every , ,
where is a -operator with parameters in the sense of Rahman \cite{qir}, and
. Unfortunately the proof of this result is
not correct. In this paper, we present a more general sharp -inequalities
for -operators which not only provide a correct proof of the
above inequality as a special case but also extend them for as
well.Comment: 16 Page
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