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A New Subclass of Analytic Functions Defined by Using Salagean q -Differential Operator

Author

Listed:
  • Muhammad Naeem

    (Department of Mathematics and Statistics, International Islamic University, 44000 Islamabad, Pakistan)

  • Saqib Hussain

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, 22060 Abbottabad, Pakistan)

  • Tahir Mahmood

    (Department of Mathematics and Statistics, International Islamic University, 44000 Islamabad, Pakistan)

  • Shahid Khan

    (Department of Mathematics, Riphah International University, 44000 Islamabad, Pakistan)

  • Maslina Darus

    (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Selangor, Malaysia)

Abstract

In our present investigation, we use the technique of convolution and quantum calculus to study the Salagean q -differential operator. By using this operator and the concept of the Janowski function, we define certain new classes of analytic functions. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, and integral mean inequalities of functions belonging to these classes are obtained and studied.

Suggested Citation

  • Muhammad Naeem & Saqib Hussain & Tahir Mahmood & Shahid Khan & Maslina Darus, 2019. "A New Subclass of Analytic Functions Defined by Using Salagean q -Differential Operator," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:458-:d:233042
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    References listed on IDEAS

    as
    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.
    2. Stanisława Kanas, 2003. "Techniques of the differential subordination for domains bounded by conic sections," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
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