q-Analogue of Differential Subordinations

Miraj Ul-Haq, Mohsan Raza, Muhammad Arif, Qaiser Khan and Huo Tang
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Miraj Ul-Haq: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Mohsan Raza: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Muhammad Arif: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Qaiser Khan: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Huo Tang: School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China

Mathematics, 2019, vol. 7, issue 8, 1-16

Abstract: 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.

Keywords: q -calculus; differential subordination; Janowski function; cardioid domain; limacon domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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