Multivalent Functions and Differential Operator Extended by the Quantum Calculus

Samir B. Hadid; Rabha W. Ibrahim; Shaher Momani

doi:10.3390/fractalfract6070354

Multivalent Functions and Differential Operator Extended by the Quantum Calculus

Samir B. Hadid
, Rabha W. Ibrahim
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Ajman University
The Institute of Electrical and Electronics Engineers (IEEE: 94086547)
University of Jordan

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.

Original language	English
Article number	354
Journal	Fractal and Fractional
Volume	6
Issue number	7
DOIs	https://doi.org/10.3390/fractalfract6070354
State	Published - Jul 2022

Keywords

analytic function
differential subordination
fractional calculus
mero-morphic functions
multivalent functions
open unit disk
quantum calculus
subordination and superordination
univalent function

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10.3390/fractalfract6070354

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title = "Multivalent Functions and Differential Operator Extended by the Quantum Calculus",

abstract = "We used the concept of quantum calculus (Jackson{\textquoteright}s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.",

keywords = "analytic function, differential subordination, fractional calculus, mero-morphic functions, multivalent functions, open unit disk, quantum calculus, subordination and superordination, univalent function",

author = "Hadid, \{Samir B.\} and Ibrahim, \{Rabha W.\} and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

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doi = "10.3390/fractalfract6070354",

language = "English",

volume = "6",

journal = "Fractal and Fractional",

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T1 - Multivalent Functions and Differential Operator Extended by the Quantum Calculus

AU - Hadid, Samir B.

AU - Ibrahim, Rabha W.

AU - Momani, Shaher

PY - 2022/7

Y1 - 2022/7

N2 - We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.

AB - We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.

KW - analytic function

KW - differential subordination

KW - fractional calculus

KW - mero-morphic functions

KW - multivalent functions

KW - open unit disk

KW - quantum calculus

KW - subordination and superordination

KW - univalent function

UR - https://www.scopus.com/pages/publications/85133132325

U2 - 10.3390/fractalfract6070354

DO - 10.3390/fractalfract6070354

M3 - Article

AN - SCOPUS:85133132325

SN - 2504-3110

VL - 6

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 7

M1 - 354

ER -

Multivalent Functions and Differential Operator Extended by the Quantum Calculus

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Keywords

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