Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

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 t...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 11; p. 2578
Main Authors: Ali, Ekram E., Srivastava, Hari M., Albalahi, Abeer M.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2023
Subjects:
a nalytic functions
Analytic functions
basic or quantum (or q-) analysis
Calculus
Complex variables
Convex analysis
Convexity
Derivatives
Graphs
Mathematical analysis
Mathematics
multivalent (or p-valent) functions
Operators (mathematics)
q-derivative operator
uniformly convex functions
uniformly starlike functions
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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 Sη,p,qn,m. Secondly, by means of this q-derivative operator, we define an interesting subclass Tℵλ,pn,m(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 κ-UCV of κ-uniformly convex functions and the class κ-UST of κ-uniformly starlike functions in U. For functions belonging to the normalized analytic and multivalent (or p-valent) function class Tℵλ,pn,m(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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11112578