Results 21 to 30 of about 306 (60)
A new inequality for a polynomial
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 11, Page 679-684, 2001., 2001 Let p(z)=a0+∑j=tnajzj be a polynomial of degree n, having no zeros in |z| < k, k ≥ 1 then it has been shown that for R > 1 and |z| = 1, |p(Rz) − p(z)| ≤ (Rn − 1)(1 + AtBtKt+1)/(1 + kt+1 + AtBt(kt+1 + k2t))max|z|=1|p(z)|−{1 − (1 + AtBtkt+1)/(1 + kt+1 + AtBt(kt+1 + k2t))}((Rn − 1)m/kn), where m = min|z|=k|p(z)|, 1 ≤ t < n, At = (Rt − 1)/(Rn − 1), and Bt =
K. K. Dewan, Harish Singh, R. S. Yadav
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Some Inequalities on Polynomials in the Complex Plane Concerning a Linear Differential Operator
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we consider new extremal problems in the uniform norm between a univariate complex polynomial and its associated reciprocal polynomial involving a generalized B‐operator. Our first result deals with inequality for the upper bound of a polynomial having s‐fold zero at the origin governed by generalized B‐operator, and as applications of ...
Mayanglambam Singhajit Singh +3 more
wiley +1 more source
Integral mean estimates for polynomials whose zeros are within a circle
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 4, Page 231-235, 2001., 2001 Let p(z) be a polynomial of degree n having all its zeros in |z| ≤ k; k ≤ 1, then for each r > 0, p > 1, q > 1 with p−1 + q−1 = 1, Aziz and Ahemad (1996) recently proved that n{∫02π|p(eiθ)|rdθ} 1/r≤{∫02π|1+keiθ|prdθ} 1/pr{∫02π|p′(eiθ)|qrdθ} 1/qr. In this paper, we extend the above inequality to the class of polynomials p(z)=anzn+∑v=μnan−vzn−v;1≤μ≤n ...
K. K. Dewan, Abdullah Mir, R. S. Yadav
wiley +1 more source
Integral mean estimates for the polar derivative of a polynomial [PDF]
, 2013 Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\leq k$ where $k\leq 1,$ then it was proved by Dewan \textit{et al} that for every real or complex number $\alpha$ with $|\alpha|\geq k$ and each $r\geq 0$ $$ n(|\alpha|-k)\left\{\int\
Gulzar, Suhail, Rather, N. A.
core
Veterinary Dermatology, Volume 36, Issue 4, Page 453-461, August 2025.Background – Canine atopic dermatitis (cAD) is a chronic, inflammatory, multifactorial and pruritic disease. The presence of skin barrier impairment (e.g. filaggrin alterations), along with abnormal immune responses, can negatively impact cutaneous barrier function.
Wendie Roldan Villalobos +5 more
wiley +1 more source
Some inequalities for maximum modules of polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 2, Page 233-238, 1991., 1990 A well‐known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z) ≠ 0 in |z| < 1, then max|z|=R≥1|p(z)|≤(Rn+12)max|z|=1|p(z)|. In this paper we prove some generalizations and refinements of this result.
N. K. Govil
wiley +1 more source
Open MathematicsIn this article, we extend inequalities concerning the polar derivative of a polynomial to integral mean for the class of polynomials with s-fold zero at the origin and the remaining zeros inside some closed disk of radius kk for k≥1k\ge 1 and k≤1k\le 1,
Singha Nirmal Kumar, Chanam Barchand
doaj +1 more source
Veterinary Dermatology, Volume 36, Issue 2, Page 148-158, April 2025.Background – Biofilm production by canine otitis externa (COE) pathogens and resistance development to multiple antimicrobials are commonly reported problems in veterinary practice. The use of adjuvants to disrupt biofilms may be a viable adjunctive therapy.
Bhumika F. Savaliya +3 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 2, Page 239-250, 1979., 1979 Suppose has radius of convergence R and . Suppose |z1| < |z2| < R, and T is either z2 or a neighborhood of z2. Put S = {N | σN(z1) > σN(z) for zϵT}. Two questions are asked: (a) can S be cofinite? (b) can S be infinite? This paper provides some answers to these questions. The answer to (a) is no, even if T = z2.
J. D. McCall, G. H. Fricke, W. A. Beyer
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Refinements of inequalities on extremal problems of polynomials
Open MathematicsLet H(z) be a polynomial of degree n, and for any complex number α, let D α H(z) = nH(z) + (α − z)H′(z) denote the polar derivative of H(z) with respect to α.
Devi Maisnam Triveni +2 more
doaj +1 more source