Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Abstract

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

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

“…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]. Our present research is a continuation of some of these earlier developments.…”

Applications of Higher-Order q-Derivative to Meromorphic q-Starlike Function Related to Janowski Function

“…The applications of q-analysis were first considered by Jackson [1,2]. In recent years, some scholars have written a number of papers [3][4][5][6][7][8][9][10][11][12][13][14][15] associated with q-starlike functions and the Janowski functions [16]. In particular, Srivastava [17,18] pointed out some applications and mathematical explanations of q-derivatives in GFT.…”