Moduli of holomorphic functions and logarithmically convex radial weights

Holomorphic Differentials as Functions of Moduli

The purpose of this note is to strengthen the results of [3 ] and to indicate a very brief derivation of some theorems announced without proof in [ l ; 3 ] . We begin by indicating a correction to [3]. Let Si and S2 be Riemann surfaces, ƒ an orientation preserving (orientation reversing) homeomorphism of bounded eccentricity of Si onto 52 and [ƒ] the homotopy class of/; then (Si, [ƒ], S2) is ca...

Some Hermite-Hadamard-like Type Inequalities for Logarithmically Convex Functions

Moduli of bounded holomorphic functions in the ball

We prove that there is a continuous non-negative function g on the unit sphere in C d, d ≥ 2, whose logarithm is integrable with respect to Lebesgue measure, and which vanishes at only one point, but such that no non-zero bounded analytic function m in the unit ball, with boundary values m⋆, has |m⋆| ≤ g almost everywhere. The proof analyzes the common range of co-analytic Toeplitz operators in...

Monotonic and Logarithmically Convex Properties of a Function Involving Gamma Functions

Generalizations of Ostrowski-like Type Integral Inequalities for s-Logarithmically Convex Functions in the First Sense

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this article, we obtain some inequalities new Ostrowski-like type integral inequalities for s-logarithmically convex functions in the first sense.