On (p, q)-Quantum Calculus Involving Quasi-Subordination

  • S. Kavitha
  • Nak Eun Cho
  • G. MurugusundaramoorthyEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


Let (p, q) ∈ (0, 1). Let the function f be analytic in |z| < 1. Further, let the (p, q) be differential operator defined as \( {\displaystyle } {{\partial _{p,q}}}f \left ( z \right ) = \frac {{f\left ( pz \right ) - f\left ( {qz} \right )}}{{z\left ( {p - q} \right )}}, \quad |z|<1. \) In the current investigation, the authors apply the (p, q)-differential operator for few subclasses of univalent functions defined by quasi-subordination. Initial coefficient bounds for the defined new classes are obtained.



The work of the first author is supported by a grant from SDNB Vaishnav College for Women under Minor Research Project scheme. The work was completed when the first author was visiting VIT Vellore Campus for a research discussion with Prof. G.Murugusundaramoorthy during the second week of November 2017.

Conflicts of Interest The authors declare that they have no conflicts of interest regarding the publication of this paper.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • S. Kavitha
    • 1
  • Nak Eun Cho
    • 2
  • G. Murugusundaramoorthy
    • 3
    Email author
  1. 1.Department of MathematicsS.D.N.B Vaishnav College for WomenChennaiIndia
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanRepublic of Korea
  3. 3.Department of Mathematics, School of Advanced SciencesVITVelloreIndia

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