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New Subclass of Analytic Function Related with Generalized Conic Domain Associated with q− Differential Operator

Author

Listed:
  • Shahid Khan
  • Saqib Hussain
  • Ilyas Khan
  • Amnah s. Al-johani
  • Mulugeta Andualem

Abstract

The quantum (or q‐) calculus is widely applied in various operators which include the q‐difference (q‐derivative) operator, and this operator plays an important role in geometric function theory (GFT) as well as in the theory of hypergeometric series. In our present investigation, we introduce and study q‐differential operator associated with q‐Mittag–Leffler function which is an extension of the Salagean q‐differential operator. By using this newly defined operator, we define a new subclass of analytic function and studied certain subclass of analytic function in generalized conic domain Ωk,q,γ. For this class, we investigate structural formula, coefficient estimates, sufficient condition, Fekete–Szegö problem, and also some subordination results.

Suggested Citation

  • Shahid Khan & Saqib Hussain & Ilyas Khan & Amnah s. Al-johani & Mulugeta Andualem, 2022. "New Subclass of Analytic Function Related with Generalized Conic Domain Associated with q− Differential Operator," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1404674
    DOI: 10.1155/2022/1404674
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    References listed on IDEAS

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    1. Saeid Shams & S. R. Kulkarni & Jay M. Jahangiri, 2004. "Classes of uniformly starlike and convex functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-3, January.
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