On a generalization of close-to-convex functions

Swadesh Kumar Sahoo, and Navneet Lal Sharma. "On a generalization of close-to-convex functions." Annales Polonici Mathematici 113.1 (2015): 93-108. <http://eudml.org/doc/280674>.

@article{SwadeshKumarSahoo2015,
abstract = {The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = \{z ∈ ℂ:|z| < 1\}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in the q-close-to-convex family. As a result we find certain dilogarithm functions that are contained in this family. Secondly, we also study the Bieberbach problem for coefficients of analytic q-close-to-convex functions. This produces several power series of analytic functions convergent to basic hypergeometric functions.},
author = {Swadesh Kumar Sahoo, Navneet Lal Sharma},
journal = {Annales Polonici Mathematici},
keywords = {-close-to-convex functions; Bieberbach problem},
language = {eng},
number = {1},
pages = {93-108},
title = {On a generalization of close-to-convex functions},
url = {http://eudml.org/doc/280674},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Swadesh Kumar Sahoo
AU - Navneet Lal Sharma
TI - On a generalization of close-to-convex functions
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 1
SP - 93
EP - 108
AB - The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in the q-close-to-convex family. As a result we find certain dilogarithm functions that are contained in this family. Secondly, we also study the Bieberbach problem for coefficients of analytic q-close-to-convex functions. This produces several power series of analytic functions convergent to basic hypergeometric functions.
LA - eng
KW - -close-to-convex functions; Bieberbach problem
UR - http://eudml.org/doc/280674
ER -