Abstract
Let P(z) be a polynomial of degree n and let α be any real or complex number, then the emanant or polar derivative of p(z) is denoted by Dαp(z) and defined as Dαp(z) = np(z) + (α − z)p 0 (z). The polynomial Dαp(z) is of degree at most n − 1 and it generalises the ordinary derivative p 0 (z) of p(z) in the sense that limα→∞ Dαp(z) α = p 0 (z). In this paper, we prove some L p inequalities for the emanant of the polynomial having all its zeros in prescribed disk. Our results generalize the earlier known results.
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