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

Abstract

This paper introduces a new integral operator in q-analog for multivalent functions. Using as an application of this operator, we study a novel class of multivalent functions and define them. Furthermore, we present many new properties of these functions. These include distortion bounds, sufficiency criteria, extreme points, radius of both starlikness and convexity, weighted mean and partial sum for this newly defined subclass of multivalent functions are discussed. Various integral operators are obtained by putting particular values to the parameters used in the newly defined operator.

Coefficient inequalities for certain subclasses of multivalent functions associated with conic domain

“…Recently, Srivastava et al (see, e.g., [15,31,34,35] published a set of papers, in which they concentrated on the class of q-starlike functions related to the Janowski functions from different aspects. For some more recent investigations on q-calculus, we refer to [13,16,27,29,33]. In this paper, we mainly generalize the work presented in Srivastava et al [32].…”

A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives

“…Additionally, the recently-published review article by Srivastava [9] is potentially useful for researchers and scholars working on these topics. For other recent investigations involving the q-calculus, one may refer to [17][18][19][20][21][22][23][24][25][26][27][28]. In this paper, we propose mainly to generalize the work presented in [29].…”

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

“…Later, q-analysis with geometrical interpretation was turned into identified through quantum groups. Due to the applications of q-analysis in mathematics and other fields, numerous researchers [3,[5][6][7][8][9][10][11][12][13][14] did some significant work on q-calculus and studied its several other applications. Recently, Srivastava [15] in his survey-cum-expository article, explored the mathematical application of q-calculus, fractional qcalculus and fractional q-differential operators in geometric function theory.…”