q-Analogue of Differential Subordinations

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.

Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

“…Following the same idea, Srivastava [29] presented some strong footing by giving some applications of q-calculus in this field by using q-analogues of hypergeometric functions. In this direction, some good valuable contributions were made by researchers, including Srivastava [30], Agrawal [31], Seoudy and Aouf [32], Agrawal and Sahoo [33], Arif and Ahmad [34], Kanas and Rȃducanu [35], Arif, Srivastava and Umar [36] and Haq et al [37]. See also the articles [38][39][40][41][42][43].…”

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

“…They made significant contributions which gradually enhanced the attractiveness of this research area for potential researchers. For more literature on quantum calculus, see [17][18][19][20][21][22][23][24][25].…”

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

“…They added significant contributions, which has slowly made this research area more attractive to forthcoming researchers. We direct the attention of our readers to [7][8][9][10][11][12] for more information. Moreover, Kanas et al [13] used Hadamad product to define the q-extension of the Ruscheweyh operator.…”