Symmetry (Oct 2024)

Applications of a <i>q</i>-Integral Operator to a Certain Class of Analytic Functions Associated with a Symmetric Domain

  • Adeel Ahmad,
  • Hanen Louati,
  • Akhter Rasheed,
  • Asad Ali,
  • Saqib Hussain,
  • Shreefa O. Hilali,
  • Afrah Y. Al-Rezami

DOI
https://doi.org/10.3390/sym16111443
Journal volume & issue
Vol. 16, no. 11
p. 1443

Abstract

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In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass.

Keywords