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Majorization Problem for q -General Family of Functions with Bounded Radius Rotations

Author

Listed:
  • Kanwal Jabeen

    (Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 45550, Pakistan)

  • Afis Saliu

    (Department of Mathematics, University of the Gambia, Serrekunda P.O. Box 3530, The Gambia)

  • Jianhua Gong

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates)

  • Saqib Hussain

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

Abstract

In this paper, we first prove the q -version of Schwarz Pick’s lemma. This result improved the one presented earlier in the literature without proof. Using this novel result, we study the majorization problem for the q -general class of functions with bounded radius rotations, which we introduce here. In addition, the coefficient bound for majorized functions related to this class is derived. Relaxing the majorized condition on this general family, we obtain the estimate of coefficient bounds associated with the class. Consequently, we present new results as corollaries and point out relevant connections between the main results obtained from the ones in the literature.

Suggested Citation

  • Kanwal Jabeen & Afis Saliu & Jianhua Gong & Saqib Hussain, 2024. "Majorization Problem for q -General Family of Functions with Bounded Radius Rotations," Mathematics, MDPI, vol. 12(17), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2605-:d:1462086
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    References listed on IDEAS

    as
    1. Afis Saliu & Khalida Inayat Noor & Saqib Hussain & Maslina Darus & Hijaz Ahmad, 2020. "On Quantum Differential Subordination Related with Certain Family of Analytic Functions," Journal of Mathematics, Hindawi, vol. 2020, pages 1-13, November.
    2. T. N. Shanmugam, 1989. "Convolution and differential subordination," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
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