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On a generalization of close-to-convex functions

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Sahoo S., Sharma N.

Annales Polonici Mathematici

2015

tom 113

nr 1

93-108

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Sahoo S.

1 Sharma N.

1 2015

Wyniki wyszukiwania

On a generalization of close-to-convex functions