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Janowski Type q -Convex and q -Close-to-Convex Functions Associated with q -Conic Domain

Author

Listed:
  • Muhammad Naeem

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

  • Saqib Hussain

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

  • Shahid Khan

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

  • Tahir Mahmood

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

  • Maslina Darus

    (Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Zahid Shareef

    (Mathematics and Natural Science, Higher Colleges of Technology, Fujairah Men’s, Fujairah 4114, UAE)

Abstract

Certain new classes of q -convex and q -close to convex functions that involve the q -Janowski type functions have been defined by using the concepts of quantum (or q -) calculus as well as q -conic domain Ω k , q [ λ , α ] . This study explores some important geometric properties such as coefficient estimates, sufficiency criteria and convolution properties of these classes. A distinction of new findings with those obtained in earlier investigations is also provided, where appropriate.

Suggested Citation

  • Muhammad Naeem & Saqib Hussain & Shahid Khan & Tahir Mahmood & Maslina Darus & Zahid Shareef, 2020. "Janowski Type q -Convex and q -Close-to-Convex Functions Associated with q -Conic Domain," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:440-:d:333694
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    References listed on IDEAS

    as
    1. Lei Shi & Qaiser Khan & Gautam Srivastava & Jin-Lin Liu & Muhammad Arif, 2019. "A Study of Multivalent q -starlike Functions Connected with Circular Domain," Mathematics, MDPI, vol. 7(8), pages 1-12, July.
    2. Sakar, F.M. & Aydoğan, M., 2018. "Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 461-468.
    3. Wasim Ul-Haq & Shahid Mahmood, 2013. "Certain Properties of a Class of Close-to-Convex Functions Related to Conic Domains," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, April.
    4. Tang, Yongchao & Zhang, Tie, 2019. "A remark on the q-fractional order differential equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 198-208.
    5. Lin-Lin Fan & Zhi-Gang Wang & Shahid Khan & Saqib Hussain & Muhammad Naeem & Tahir Mahmood, 2019. "Coefficient Bounds for Certain Subclasses of q -Starlike Functions," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    6. Hai-Yan Zhang & Rekha Srivastava & Huo Tang, 2019. "Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    7. K. G. Subramanian & T. V. Sudharsan & Herb Silverman, 2003. "On uniformly close-to-convex functions and uniformly quasiconvex functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-6, January.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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