Locally univalent functions in the unit disk

Harmonic Functions in the Unit Disk

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

Notes on functions on the unit disk

As usual, R denotes the real numbers, Z denotes the integers, and C denotes the complex numbers. Thus each α ∈ C can be expressed as a + b i, where a, b are real numbers and i = −1. We call a, b the real and imaginary parts of α, and denote them Reα, Imα, respectively. If z is a complex number, with z = x + y i where x, y are the real and imaginary parts of z, then we write z for the complex co...

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Univalent Functions with Univalent Derivatives. Ii

Valence and Oscillation of Functions in the Unit Disk

We investigate the number of times that nontrivial solutions of equations u′′ + p(z)u = 0 in the unit disk can vanish—or, equivalently, the number of times that solutions of S(f) = 2p(z) can attain their values—given a restriction |p(z)| ≤ b(|z|). We establish a bound for that number when b satisfies a Nehari-type condition, identify perturbations of the condition that allow the number to be in...