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q-Analogue of Differential Subordinations

School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 724;
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.

AMA Style

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

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.

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