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On q-Uniformly Mocanu Functions

Department of Mathematics, COMSATS, University Islamabad, Islamabad 44000, Pakistan
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(1), 5; https://doi.org/10.3390/fractalfract3010005
Received: 28 January 2019 / Revised: 6 February 2019 / Accepted: 10 February 2019 / Published: 11 February 2019
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Abstract

Let f be analytic in open unit disc E = { z : | z | < 1 } with f ( 0 ) = 0 and f ( 0 ) = 1 . The q-derivative of f is defined by: D q f ( z ) = f ( z ) f ( q z ) ( 1 q ) z , q ( 0 , 1 ) , z B { 0 } , where B is a q-geometric subset of C . Using operator D q , q-analogue class k U M q ( α , β ) , k-uniformly Mocanu functions are defined as: For k = 0 and q 1 , k reduces to M ( α ) of Mocanu functions. Subordination is used to investigate many important properties of these functions. Several interesting results are derived as special cases. View Full-Text
Keywords: q-calculus; q-starlike; uniformly convex; subordination; Mocanu functions; q-Ruscheweyh derivative q-calculus; q-starlike; uniformly convex; subordination; Mocanu functions; q-Ruscheweyh derivative
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Badar, R.S.; Noor, K.I. On q-Uniformly Mocanu Functions. Fractal Fract 2019, 3, 5.

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