2 citations · 4 across the 6 of their papers we have counts for
7 papers
On harmonic convolutions involving a vertical strip mapping
Raj Kumar, Sushma Gupta, Sukhjit Singh +1
Let f_β= h_β+\bar{g}_βand F_a = H_a +\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_β+g_β= 1/(2i\sinβ)log((1 + ze^{iβ})/(1 + ze^{-iβ})), 0<β<πand H_a+G_…
An application of Cohn's rule to convolutions of univalent harmonic mappings
Raj Kumar, Sushma Gupta, Sukhjit Singh +1
Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_β= h_β+ \bar{g}_β, where f_βis obtained by shearing of analytic…
Convolution properties of some harmonic mappings in the right-half plane
Raj Kumar, Michael Dorff, Sushma Gupta +1
Dorff, proved in [2] that the convolution of two harmonic right-half plane mappings is convex in the direction of real axis provided that the convolution is locally univalent and s…
Typically Real Harmonic Functions
Michael Dorff, Maria Nowak, Wojciech Szapiel
We consider a class $\THO$ of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some pa…
Convolutions of harmonic convex mappings
Michael Dorff, Maria Nowak, Magdalena Woloszkiewicz
The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right half-plane mapping or a normalized vertical stri…
Derivative relationships between volume and surface area of compact regions in R^d
Jean-Luc Marichal, Michael Dorff
We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r = d V/A. We show that the families of regions for…