A certain subclass of meromorphically q-starlike functions associated with the Janowski functions

Abstract

In this paper, the authors introduce a new subclass of meromorphic q-starlike functions which are associated with the Janowski functions. A characterization of meromorphically q-starlike functions associated with the Janowski functions has been obtained when the coefficients in their Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, partial sums, and the radius of starlikeness estimates for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

“…The values of Q 1 and Q 2 are given by (13) and (14), respectively, and that of Φ 2 is given in (7).…”

“…Many researchers contributed to the development of the theory by introducing certain classes with the help of q-calculus. For some details about these contributions, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. We contribute to the subject by studying the q-integral operator in the conic region.…”

Some general families of q-starlike functions associated with the Janowski functions

“…On the other hand, Srivastava et al [18] investigated the Hankel determinant of a subclass of bi-univalent functions defined by using a symmetric q-derivative. Mahmood et al [10] studied the class of q-starlike functions in the conic region, while Srivastava et al [21] and Mahmood et al [9] studied several families of q-starlike functions related with the celebrated Janowski functions (see also [11]). The upper bound of the third Hankel determinant for the class of q-starlike functions was investigated in [12].…”

Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

“…Recently Srivastava et al [13] (see also [14]) successfully combined the concept of Janowski [15] and the above mentioned q-calculus and introduced the class…”