Inequalities for the Polar Derivative of a Polynomial

Shakeri, M.; Bidkham, M.; Gordji, M. Eshaghi

doi:10.48550/arxiv.0907.2836

Search citation statements

Order By: Relevance

Paper Sections

Select...

Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Concerning the inequalities for |D α P (z)| in terms of |P (z)| an interested reader may go through [9,11], [14]- [17]. Now, the following result is regarding the growth of polar derivative of a polynomial.…”

Section: Resultsmentioning

confidence: 99%

L^q inequalities for polynomials with restricted zeros concerning the growth

Rashid,

Shah

2024

GJOM

View full text Add to dashboard Cite

If Pn denotes the class of polynomials of degree at most n, then for P ∈ Pn, a consequence of Maximum Modulus theorem yields for R > 1, || P(R, )||∞ < Rn || P ||∞. Various generalizations and refinements of this result are available in literature. In this paper, we consider a general class of polynomials Pn, μ, 1 < μ < n, with restriction on zeros in a specific way and obtain Zygmund-type inequalities concerning the growth of polynomials. Besides obtaining a refinement of a result due to Aziz and Shah, we improve a result of Aziz and Rather.

show abstract