Improved Bohr inequality for harmonic mappings

Coefficient inequality for perturbed harmonic mappings

Matrix Order in Bohr Inequality for Operators

The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogr...

Improved Cramer-Rao Inequality for Randomly Censored Data

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...

Harmonic Mappings of Spheres

Introduction and statement of results. This announcement describes an elementary method of constructing harmonic maps in some cases not covered by the general existence theory. Recall that given smooth Riemannian manifolds N and M, with N compact, then the energy functional E:H(N,M) -> R is defined on a suitable manifold of maps H(iV, M ) and is given by E{ f ) = \ \n \df | . A map ƒ is said to...

Harmonic Mappings between Riemannian

Harmonic mappings between two Riemannian manifolds is an object of extensive study, due to their wide applications in mathematics, science and engineering. Proving the existence of such mappings is challenging because of the non-linear nature of the corresponding partial differential equations. This thesis is an exposition of a theorem by Eells and Sampson, which states that any given map from ...