ANALYTIC FUNCTIONS WITH CONIC DOMAINS ASSOCIATED WITH CERTAIN GENERALIZED q-INTEGRAL OPERATOR

Ahuja O. P., Çetinkaya A., Jain N. K.

Communications of the Korean Mathematical Society, vol.38, no.4, pp.1111-1126, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.4134/ckms.c230002
  • Journal Name: Communications of the Korean Mathematical Society
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.1111-1126
  • Keywords: coefficient estimates, conic domains, k-uniformly starlike functions of order gamma, q-derivative operator, q-difference operator, q-gamma function, q-integral operator, Quantum calculus
  • Istanbul Kültür University Affiliated: Yes

Abstract

In this paper, we define a new subclass of k-uniformly star-like functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous sub-class of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.