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An inequality for the polar derivative of a polynomial
... Abstract: In this paper, an inequality for the polar derivative of a polynomial with restricted zeros is obtained, which refines and generalizes some well known polynomial inequalities[r] ... See full document
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Location of zeros of polar derivative of polynomial with real coefficients
... “Location Location of zeros of polar derivative of polynomial with real coefficients coefficients”, International Journal of Current Research,, 7, 11, 1 23144-23150... INTRODUCTION To es[r] ... See full document
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Inequalities for the Polar Derivative of a Polynomial
... Inequalities for the Polar Derivative of a Polynomial Gulshan Singh1, Wali Mohammad Shah2, Yash Paul1 Bharathiar University Coimbatore, Tamil Nadu, India Department of Mathematics, Kashm[r] ... See full document
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Polar Derivative Versions of Polynomial Inequalities
... D p z α = np z + α − z p z denote the polar derivative of the polynomial p z ( ) with respect to α . In this paper, first we extend as well as generalize the result proved by Dewan and Mir [Inter. ... See full document
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On the maximum modulus of a polynomial and its polar derivative
... On the maximum modulus of a polynomial and its polar derivative Ahmad Zireh Correspondence: [email protected] Department of Mathematics, Shahrood University of Technology, Shahrood[r] ... See full document
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Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial
... MSC: 26D15 Keywords: majorization; n-convexity; Schur-convexity; Sherman’s theorem; Lidstone interpolating polynomial; Čebyšev functional; Grüss type inequalities; Ostrowsky type inequa[r] ... See full document
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A new inequality for a polynomial
... Inequality (1.1) is a famous result known as Bernstein’s inequality (see [9]) where as inequality (1.2) is a simple consequence of maximum modulus principle [7]. Here in both inequalities (1.1) and ... See full document
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A generalized inequality for the polar derivative of a polynomial
... known polynomial inequalities. Theorem Let P(z) be a polynomial of degree n that does not vanish in | z | < k, k ≤ , then for all real or complex numbers α i with | α i | ≥ k, k ≤ , i = , , ... See full document
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Inequalities for the Polar Derivative of a Polynomial
... Combining 3.4 and 3.6 we get the desired result. This completes the proof of inequality 1.12. The proof of the Theorem in the case n 3 follows along the same lines as the proof of 1.12 but instead of inequalities ... See full document
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On the Zeros of the Polar Derivative of a Polynomial
... Reddy, On the Zeros of Polar Derivatives, International Journal of Recent Research in Mathematics, Computer Science and Information Technology, Vol.2, Issue 1 April 2015- September 2015,[r] ... See full document
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About some exponential inequalities related to the sinc function
... 3.2 Inequalities with polynomial exponents In this subsection, we propose and prove a new double-sided inequality involving the sinc function with polynomial exponents.. To be more speci[r] ... See full document
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Inequalities for a polynomial and its derivative
... Inequality (.) was conjectured by Erdös and later proved by Lax [], whereas inequality (.) was proved by Ankeny and Rivlin [], for which they made use of (.). Both these inequalities are also sharp, ... See full document
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GENERALIZATION OF SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF POLYNOMIALS WITH RESTRICTED ZEROS
... the polynomial p(z) having all zeros in |z| ≤ k, k ≥ 1 with s-fold zeros at the origin, therefore q(z) = z n p(1/z) is a polynomial of degree (n − s) which does not vanish in |z| < 1/k, where 1/k ≤ ... See full document
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On the $s^{th}$ Derivative of a Polynomial-II
... Inequality (1.3) was conjectured by Erd¨ os and later verified by Lax[11], whereas inequality (1.4) was proved by De-Bruijn[7] for r ≥ 1. Rahman and Schemeisser[13] later proved that (1.4) holds for 0 < ... See full document
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On the maximum modulus of a polynomial and its derivative
... Proof. By using the inequality |p(z)| ≤ |F(z)| for |z| = 1, any zero of F(z) that lies on |z| = 1, is the zero of p(z). On the other hand, from Rouche’s Theorem, it is obvious that for α with |α | < 1, F(z) + α ... See full document
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Constantin’s inequality for nabla and diamond alpha derivative
... Constantin’s inequality on time scales that is an important tool used in determining some properties of various dynamic equations such as global existence, uniqueness and ...Constantin’s inequality is ... See full document
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New error inequalities for the Lagrange interpolating polynomial
... Remark 3.2. The above estimate has only theoretical importance, since it is difficult to find the polynomial P ∗ . In fact, we can find P ∗ only for some special cases of functions. However, we can use the estimate ... See full document
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<p>Identification Of Natural Compound Derivative For Inhibition Of XLF And Overcoming Chemoresistance In Colorectal Cancer Cells</p>
... Upon treatment of 5 μ M G3 before NHEJ assay, HCT116 5-Fu-R and HCT116 OXA-R exhibited NHEJ ef fi ciency almost equivalent to that in HCT116 WT ( Figure 3A ), suggesting G3 sensitizes 5-F[r] ... See full document
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Sherman’s and related inequalities with applications in information theory
... majorization inequality and Jensen’s inequality which can be used to derive some new estimates for some entropies and measures between probabil- ity ... See full document
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A Perturbed Trapezoid Inequality in Terms of the Third Derivative and Applications
... Atkinson [1] terms the quadrature rule (2.2) a connected trapezoidal rule and obtains it using an asymptotic error estimate approach which does not provide an expression for the error bo[r] ... See full document
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