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Distortion Inequalities for Ruscheweyh Derivatives [PDF]
Mathematical Inequalities & Applications, 1998 Let \(A\) denote the class of functions \(f(z)\) which are analytic in the open unit disk \(U\) with \(f(0)=0\) and \(f'(0)=1\). For \(f(z)\in A\), the Ruscheweyh derivative of order \(\lambda\) is denoted by \(D^\lambda f(z)\). The object of the present paper is to derive several distortion inequalities involving \(D^\lambda f(z)\) for certain classes
Owa, Shigeyoshi, Srivastava, H. M.
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n-derivations and functional inequalities with applications [PDF]
Mathematical Inequalities & Applications, 2020 Summary: We prove that every bounded \(n\)-derivation of a commutative factorizable Banach algebra maps into its radical. Also, the nilpotency of eigenvectors of any bounded \(n\)-derivation corresponding to its eigenvalues is derived. We introduce the notion of approximaten-derivations on a Banach algebra \(\mathscr{A}\) and show that the separating ...
Alinejad, Ahmad +2 more
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Inequalities for the Derivative of a Polynomial [PDF]
Proceedings of the American Mathematical Society, 1983 Let P ( z ) =
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Inequalities for the derivatives [PDF]
Mathematical Inequalities & Applications, 2000 It is proved that one cannot approximate stably the first derivative of a smooth function given noisy values of this function and a bound on this function and its first derivative. Such an approximation is shown to be possible if an a priori bound is known for a fractional derivative of order greater than one. An algorithm is proposed for such a stable
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Inequalities for a polynomial and its derivative
Journal of Mathematical Analysis and Applications, 2007 Let \(p(z)=a_0+\sum^n_{\nu=\mu}a_\nu z^\nu\), \(1\leq \mu\leq n\), be a polynomial of degree \(n\) such that \(p(z)\neq 0\) in \(|z|0\).
Chanam, Barchand, Dewan, K. K.
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Some Identities and Inequalities for Derivatives
Journal of Approximation Theory, 1995 The authors reprove inequalities due to Bernstein and Brudnyi, respectively, and prove a few other new inequalities involving the derivatives of trigonometric or algebraic polynomials. These proofs are based on the following identity due to \textit{M. Riesz} [Jahresber. Dtsch. Math.-Ver. 23, 354-368 (1914; J.-buch F.d.M.
Balazs, K., Kilgore, T.
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On Inequalities of Periodic Functions and Their Derivatives [PDF]
Proceedings of the American Mathematical Society, 1983 The inequality ‖ f ‖
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Inequalities for the Polar Derivative of a Polynomial
Journal of Inequalities and Applications, 2009 In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J. Pure Appl. Math.
M. Bidkham +2 more
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An inequality for the derivative of self-inversive polynomials [PDF]
Bulletin of the Australian Mathematical Society, 1983 In this paper it is shown that if p(z) is a polynomial of degree n satisfying thenThe result is best possible.
Dewan, K. K., Govil, N. K.
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Inequalities for the Polar Derivative of a Polynomial [PDF]
Abstract and Applied Analysis, 2012 For a polynomial p(z) of degree n, we consider an operator Dα which map a polynomial p(z) into Dαp(z): = (α − z)p′(z) + np(z) with respect to α. It was proved by Liman et al. (2010) that if p(z) has no zeros in |z | < 1, then for all α, β ∈ ℂ with |α | ≥ 1, | β | ≤ 1 and |z | = 1, |zDαp(z) + nβ((|α | − 1)/2)p(z)|≤(n/2){[|α + β((|α | − 1 ...
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