Second Hankel Determinant for a Class of Analytic Functions Defined by a Fractional Operator
- Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions. Prokhorov, V.A.; Saff, E.B. // Constructive Approximation;1999, Vol. 15 Issue 2, p155
In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class R[SUBn,m] of all rational functions of order(n, m) are considered. Let ?[SUBn,m] = ?[SUBn,m](f; E) be the distance of f in the...
- Measurement of shear elasticity and viscosity of rubberlike materials. Andreev, V.; Burlakova, T. // Acoustical Physics;Jan2007, Vol. 53 Issue 1, p44
The method and results of measuring the shear elastic modulus of a rubberlike polymer by the deformation of a plane elastic layer are described. For shear deformations not exceeding 0.5 of the layer thickness, the shear modulus is constant and its value is in agreement with the value determined...
- SOME UNIVALENCE CONDITIONS FOR AN INTEGRAL OPERATOR. PESCAR, Virgil // Bulletin of the Transilvania University of Brasov, Series III: M;2013, Vol. 6 Issue 55-1, p55
In this work we define a general integral operator for analytic functions in the open unit disk and we derive some conditions for univalence of this integral operator.
- GENERALIZED HANKEL OPERATORS ON THE WHITE NOISE DISTRIBUTIONS. Horrigue, Samah; Ouerdiane, Habib // Communications in Mathematical Analysis;2008, Vol. 4 Issue 2, p19
In this paper we introduce and investigate Hankel operators on infinite dimensional entire functionals with growth conditions. First, we prove that this generalized Hankel operator is well defined and is a continuous operator. Then, we show that the associated form, usually defined on the...
- Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative. Mishra, A. K.; Gochhayat, P. // International Journal of Mathematics & Mathematical Sciences;2008, p1
By making use of the fractional differential operator Î©zÎ» due to Owa and Srivastava, a class of analytic functions RÎ»(Î±, Ï) (0 â‰¤ Ï â‰¤ 1, 0 â‰¤ Î» < 1, âˆ£Î±âˆ£ < 2) is introduced. The sharp bound for the nonlinear functional âˆ£a2a4 - a32âˆ£ is...
- Hankel operators and invariant subspaces of the Dirichlet space. Shuaibing Luo; Richter, Stefan // Journal of the London Mathematical Society;Apr2015, Vol. 91 Issue 2, p423
The Dirichlet space D is the space of all analytic functions f on the open unit disc D such that f' is square integrable with respect to two-dimensional Lebesgue measure. In this paper, we prove that the invariant subspaces of the Dirichlet shift are in one-to-one correspondence with the kernels...
- Coefficient inequality for uniformly convex functions of order Î±. Vamshee Krishna, D.; Ramreddy, T. // Journal of Advanced Research in Pure Mathematics;2013, Vol. 5 Issue 1, p25
The objective of this paper is to obtain an upper bound to the second Hankel determinant âˆ£a2a4 - a32âˆ£ for the function f and its inverse belonging to the uniformly convex functions of order Î±(0 â‰¤ Î± < 1), using Toeplitz determinants.
- A Novel Filled Function Method and Quasi-Filled Function Method for Global Optimization. Wu, Z. Y.; Lee, H. W. J.; Zhang, L. S.; Yang, X. M. // Computational Optimization & Applications;Jun2006, Vol. 34 Issue 2, p249
This paper gives a new definition of a filled function, which eliminates certain drawbacks of the traditional definitions. Moreover, this paper proposes a quasi-filled function to improve the efficiency of numerical computation and overcomes some drawbacks of filled functions. Then, a new filled...
- Certain Sufficient Conditions for Univalence of Two Integral Operators. Frasin, B. A. // European Journal of Pure & Applied Mathematics;2010, Vol. 3 Issue 6, p1141
In this paper, we obtain new sufficient conditions for two general integral operator to be univalent in the open unit disc. A number of new univalent conditions would follow upon specializing the parameters involved in our main results.