Harmonic close-to-convex mappings associated with Sălăgean q-differential operator

Mishra O., Çetinkaya A., Sokół J.

Studia Universitatis Babes-Bolyai Mathematica, vol.70, no.1, pp.33-49, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.24193/subbmath.2025.1.03
  • Journal Name: Studia Universitatis Babes-Bolyai Mathematica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.33-49
  • Keywords: analytic functions, harmonic functions, partial sums, Sălăgean q-differential operator
  • Istanbul Kültür University Affiliated: Yes

Abstract

In this paper, we define a new subclass (Formula presented) of analytic functions and a new subclass (Formula presented) of harmonic functions (Formula presented) associated with Sălăgean q-differential operator. We prove that a harmonic function (Formula presented) belongs to the class (Formula presented) if and only if the analytic functions h+∊g belong to (Formula presented) for each ∊ (|∊| = 1), and using a method by Clunie and Sheil-Small, we determine a sufficient condition for the class (Formula presented) to be close-to-convex. We provide sharp coefficient estimates, sufficient coefficient condition, and convolution properties for such functions classes. We also determine several conditions of partial sums of (Formula presented).