Subclasses of p-valent k-uniformly convex and starlike funcitons defined by the q-derivative operator
Date
2023
Authors
Ali, Ekram E.
Srivastava, Hari M.
Albalahi, Abeer M.
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator Sⁿₙ ₚᵐq. Secondly, by means of this q-derivative operator, we define an interesting subclass Tℵⁿₗ,ᵐₚ(η,α,κ) of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk U. This p-valent analytic function class is associated with the class k-UCV of k-uniformly convex functions and the class k-UST of k-uniformly starlike functions in U. For functions belonging to the normalized analytic and multivalent (or p-valent) function class Tℵⁿₗ,ᵐₚ(η,α,κ), we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein.
Description
Keywords
a nalytic functions, multivalent (or p-valent) functions, uniformly convex functions, uniformly starlike functions, basic or quantum (or q-) analysis, q-derivative operator, hadamard product (or convolution), generalized q-hypergeometric function
Citation
Ali, E. E., Srivastava, H. M., & Albalahi, A. M. (2023). Subclasses of p-valent κ-uniformly convex and starlike functions defined by the q-derivative operator. Mathematics, 11(11), 2578. https://doi.org/10.3390/math11112578