On a generalization of close-to-convex functions

• Autorzy: Swadesh Kumar Sahoo , Navneet Lal Sharma
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30C50: Coefficient problems for univalent and multivalent functions
• 30B10: Power series (including lacunary series)
• 40A30: Convergence and divergence of series and sequences of functions
• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 33B30: Higher logarithm functions
• 30C55: General theory of univalent and multivalent functions
• 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)
• 33D15: Basic hypergeometric functions in one variable, r φ s

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 113
• Numer: 1
• Strony: 93-108

Daty

wydano

2015

Twórcy

autor

Swadesh Kumar Sahoo

• Department of Mathematics, Indian Institute of Technology Indore, Indore 452 017, India

autor

Navneet Lal Sharma

• Department of Mathematics, Indian Institute of Technology Indore, Indore 452 017, India

Identyfikatory

DOI

10.4064/ap113-1-6