On the (p, q)-Lucas polynomial coefficient bounds of the bi-univalent function class sigma


ALTINKAYA Ş., Yalcin S.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, vol.25, no.3, pp.567-575, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1007/s40590-018-0212-z
  • Journal Name: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Page Numbers: pp.567-575
  • Keywords: (p, q)-Lucas polynomials, Coefficient bounds, Bi-univalent functions, FIBONACCI, SUBCLASS

Abstract

The idea of the present paper stems from the work of Lee and Ac (J Appl Math 2012:1-18, 2012). We want to remark explicitly that, in our article, by using the (p, q)-Lucas polynomials, our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, we aim at introducing a new class of bi-univalent functions defined through the (p, q)-Lucas polynomials. Furthermore, we derive coefficient inequalities and obtain Fekete-Szego problem for this new function class.