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Inequality for polynomials with prescribed zeros

Jain Vinay Kumar

Journal of Mathematics and Applications

2020

Vol. 43

81--85

For a polynomial p(z) of degree n with a zero at β,of order at least k(≥1), it isknown that [wzór]. By considering polynomial p(z) of degree n in the form [wzór], a polynomial of degree n−k, with [wzór] we have obtained [wzór] a generalization of the known result.

On the derivative of a polynomial with prescribed zeros

Jain V. K.

Journal of Mathematics and Applications

2017

Vol. 40

97--120

For a polynomial [wzór] of degree n having all its zeros in │z│ ≤ K, K ≥1 it is known that max [wzór]. By assuming a possible zero of order m, 0 ≤ m ≤ n - 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.

On the zeros of an analytic function

Jain V.

Journal of Mathematics and Applications

2014

Vol. 37

51--58