A Subfamily of Univalent Functions Associated with q-Analogue of Noor Integral Operator

Abstract

The main objective of the present paper is to define a new subfamily of analytic functions using subordinations along with the newly defined -Noor integral operator. We investigate a number of useful properties such as coefficient estimates, integral representation, linear combination, weighted and arithmetic means, and radius of starlikeness for this class.

A Study of Multivalent q-starlike Functions Connected with Circular Domain

“…Recently, a new idea was presented by Darus [21] and introduced a new differential operator called generalized q-differential operator with the help of q-hypergeometric functions where they studied some useful applications of this operator. For the recent extension of different operators in q-analogue, see the references [2,9,8]. The operator defined in [17] was extended further for multivalent functions by Arif et al [10] in which they investigated its important applications.…”

“…Now when q → 1 − , the operator defined in (1.6) becomes to the familiar differential operator investigated in [12] and further, setting p = 1, we get the most familiar operator known as Ruscheweyh operator [24] (see also [3,22]). Also, for different types of operators in q-analogue, see the works [2,4,6,7,9,21].…”

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

“…Recently, new thoughts by Maslina in [17] were used to create a novel differential operator called generalized q-differential operator with the help of q-hypergeometric functions where the authors conducted an in-depth study of applications of this operator. For further information on the extensions of different operators in q-analog, we direct the readers to [18][19][20][21][22]. The aim of the present article is to introduce a new integral operator in q-analog for multivalent functions using Hadamard product and then study some of its useful applications.…”

q-Analogue of Differential Subordinations

“…Many researchers contributed in the development of the theory by introducing certain classes with the help of q-calculus. For some details about these contributions, see [25][26][27][28].…”