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, cilt.38, sa.4, ss.1111-1126, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.4134/ckms.c230002
  • Dergi Adı: Communications of the Korean Mathematical Society
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.1111-1126
  • Anahtar Kelimeler: 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
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

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.