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Article

q-Analogue of Differential Subordinations

1
School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China
2
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
3
Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 724; https://doi.org/10.3390/math7080724
Received: 24 June 2019 / Revised: 6 August 2019 / Accepted: 8 August 2019 / Published: 9 August 2019
In this article, we study differential subordnations in q-analogue. Some properties of analytic functions in q-analogue associated with cardioid domain and limacon domain are considered. In particular, we determine conditions on α such that 1 + α z q h z h z n ( n = 0 , 1 , 2 , 3 ) are subordinated by Janowski functions and h z 1 + 4 3 z + 2 3 z 2 . We also consider the same implications such that h z 1 + 2 z + 1 2 z 2 . We apply these results on analytic functions to find sufficient conditions for q-starlikeness related with cardioid and limacon. View Full-Text
Keywords: q-calculus; differential subordination; Janowski function; cardioid domain; limacon domain q-calculus; differential subordination; Janowski function; cardioid domain; limacon domain
MDPI and ACS Style

Ul-Haq, M.; Raza, M.; Arif, M.; Khan, Q.; Tang, H. q-Analogue of Differential Subordinations. Mathematics 2019, 7, 724. https://doi.org/10.3390/math7080724

AMA Style

Ul-Haq M, Raza M, Arif M, Khan Q, Tang H. q-Analogue of Differential Subordinations. Mathematics. 2019; 7(8):724. https://doi.org/10.3390/math7080724

Chicago/Turabian Style

Ul-Haq, Miraj, Mohsan Raza, Muhammad Arif, Qaiser Khan, and Huo Tang. 2019. "q-Analogue of Differential Subordinations" Mathematics 7, no. 8: 724. https://doi.org/10.3390/math7080724

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