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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics (Basel) Jg. 11; H. 11; S. 2578
Hauptverfasser: Ali, Ekram E., Srivastava, Hari M., Albalahi, Abeer M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.06.2023
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math11112578