Mathematics (Mar 2023)

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using <i>q</i>-Calculus

  • Ridong Wang,
  • Manoj Singh,
  • Shahid Khan,
  • Huo Tang,
  • Mohammad Faisal Khan,
  • Mustafa Kamal

DOI
https://doi.org/10.3390/math11051217
Journal volume & issue
Vol. 11, no. 5
p. 1217

Abstract

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In this investigation, the q-difference operator and the Sălăgean q-differential operator are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine the general Taylor–Maclaurin coefficient of the functions in this class using the Faber polynomial method. We demonstrate the unpredictable behaviour of initial coefficients a2, a3 and investigate the Fekete–Szegő problem a3−a22 for the subclasses of bi-close-to-convex functions. To highlight the connections between existing knowledge and new research, certain known and unknown corollaries are also highlighted.

Keywords