An annular function whose derivative is not annular.
An application of a subordination chain.
An Application of Convolution Integral
MSC 2010: 30C45Applying the Bernardi integral operator, an interesting convolution integral is introduced. The object of the present paper is to derive some convolution integral properties of functions f(z) to be in the subclasses of the classes S*(α) and Κ(α) by making use of their coefficient inequalities.
An application of differential subordination.
An application of differential subordinations, II
An application of fine potential theory to prove a Phragmen Lindelöf theorem
We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset of the complex plane: if is analytic on , bounded near the boundary of , and the growth of is at most polynomial then either is bounded or for some positive and has a simple pole.
An application of Hölder's inequality for convolutions.
An application of hypergeometric functions to a problem in function theory.
An application of Kronecker' s theorem to rational functions.
An application of metric diophantine approximation in hyperbolic space to quadratic forms.
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...
An application of Miller and Mocanu's result.
An application of subordination on harmonic function.
An application of the generalized Bessel function
We introduce and study some new subclasses of starlike, convex and close-to-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.
An application of the Ruscheweyh derivatives.
An application of the Ruscheweyh derivatives. II.
An Application of the Subordination Chains
MSC 2010: 30C45, 30A20, 34A30The notion of differential superordination was introduced in [4] by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination [3] and was developed in [5]. The notion of strong differential subordination was introduced by J.A. Antonino and S. Romaguera in [1]. In [6] the author introduced the dual concept of strong differential superordination. In this paper we study strong differential superordination using the subordination chains.
An application of the topological rigidity of the sine family.
An Approximate Riemann Mapping Theorem in Cn.
An Approximate Taylor's Theorem for R(X).
An area inequality for quasi-subordinate analytic functions