Some Lp Inequalities for B-Operators - Applied Mathematics

AM > Vol.4 No.1, January 2013

Some L_p Inequalities for B-Operators ()

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Download as PDF (Size: 303KB) PP. 155-166

DOI: 10.4236/am.2013.41026 3,212 Downloads 5,053 Views Citations

Author(s)

Nisar Ahmad Rather, Sajad Hussain Ahangar

Affiliation(s)

Department of mathematics, University of Kashmir, Harzarbal, Sringar, India..

ABSTRACT

If P(z) is a polynomial of degree at most n having all its zeros in

, then it was recently claimed by Shah and Liman ([1], estimates for the family of $B$-operators, Operators and Matrices, (2011), 79-87) that for every R≧1, p ≧ 1,

where B is a B_n-operator with parameters

in the sense of Rahman [2], and

. Unfortunately the proof of this result is not correct. In this paper, we present certain more general sharp Lp-inequalities for Bn-operators which not only provide a correct proof of the above inequality as a special case but also extend them for 0≦p﹤1 as well.

KEYWORDS

L^p -Inequalities; B_n-Operators; Polynomials

Share and Cite:

N. Rather and S. Ahangar, "Some L_p Inequalities for B-Operators," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 155-166. doi: 10.4236/am.2013.41026.

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