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

Kanwal Jabeen, Afis Saliu, Jianhua Gong () and Saqib Hussain
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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

Mathematics, 2024, vol. 12, issue 17, 1-11

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.

Keywords: q-calculus; subordination; majorization; functions of bounded radius rotation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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