Abstract
A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper.
Highlights
The q-calculus is classical calculus without the concept of limit
Aral [4] and Anastassiou and Gal [5,6] generalized some complex operators which are known as the q-Picad and the q-Gauss–Weierstrass singular integral operators
Srivastava et al [7] have written a series of articles [8,9,10] in which they combined the q-difference operator and the Janowski functions to define new function classes and studied their useful properties from different viewpoints
Summary
The q-calculus is classical calculus without the concept of limit. In recent years, qcalculus has attracted great attention of scholars on account of its applications in the research field of physics and mathematics as, for example, in the study of quantum groups, q-deformed superalgebras, fractals and multifractal measures, optimal control problems and in chaotic dynamical systems. Let A p denote the class of p-valent analytic functions f (z) given by the following A function f (z) ∈ A p is known as a p-valent convex function of order δ and is denoted by f (z) ∈ C p (δ), if it meets the following condition: z f 00 (z)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
