Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator

Abstract

In analysis, the introduction of q-calculus has been a revelation. It has a deep impact on various concepts and applications of pure and applied sciences. In this article we investigate certain geometric properties relating to convolution of functions of a newly defined class of analytic functions. The important region of the lemniscate of Bernoulli is considered. Here we utilize concepts of q-calculus which enhances and generalizes the vitality of this research work. In the same context we study the Fekete–Szegö problem.

Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

“…Note that H 2,1 (f) = a 3 − a 2 2 , is classical Fekete-Szegö functional. In year 1933, the maximum value of |H 2,1 (f)| was obtained for a class S. For various subclasses of class A, the maximum value of |H 2,1 (f)| was investigated by different authors, for details see [7,[16][17][18][19][29][30][31][32][33][34]. Furthermore, second Hankel determinant when j = 2 and k = 2 is…”

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

“…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].…”

A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences

“…More recently, Srivastava et al [11,12] first defined certain subclasses of q-starlike functions and then studied their various properties including for example some coefficient inequalities, inclusion properties, and a number of sufficient conditions. Moreover, the subclasses of q-starlike functions associated with the Janwoski or some other functions have been studied by the many authors (see, for example, [13][14][15][16][17][18][19][20]). For some more recent investigations based upon the q-calculus, we may refer the interested reader to the works in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”