Multivalent Functions and Differential Operator Extended by the Quantum Calculus
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 funct...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/7/354 |
| _version_ | 1797433577198059520 |
|---|---|
| author | Samir B. Hadid Rabha W. Ibrahim Shaher Momani |
| author_facet | Samir B. Hadid Rabha W. Ibrahim Shaher Momani |
| author_sort | Samir B. Hadid |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T10:17:58Z |
| format | Article |
| id | doaj.art-12344887d0a04bb4b691c686d95a7855 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T10:17:58Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-12344887d0a04bb4b691c686d95a78552023-12-01T22:10:25ZengMDPI AGFractal and Fractional2504-31102022-06-016735410.3390/fractalfract6070354Multivalent Functions and Differential Operator Extended by the Quantum CalculusSamir B. Hadid0Rabha W. Ibrahim1Shaher Momani2Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab EmiratesThe Institute of Electrical and Electronics Engineers (IEEE: 94086547), Portland, OR 13765, USADepartment of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab EmiratesWe 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.https://www.mdpi.com/2504-3110/6/7/354quantum calculusanalytic functionsubordination and superordinationdifferential subordinationunivalent functionopen unit disk |
| spellingShingle | Samir B. Hadid Rabha W. Ibrahim Shaher Momani Multivalent Functions and Differential Operator Extended by the Quantum Calculus Fractal and Fractional quantum calculus analytic function subordination and superordination differential subordination univalent function open unit disk |
| title | Multivalent Functions and Differential Operator Extended by the Quantum Calculus |
| title_full | Multivalent Functions and Differential Operator Extended by the Quantum Calculus |
| title_fullStr | Multivalent Functions and Differential Operator Extended by the Quantum Calculus |
| title_full_unstemmed | Multivalent Functions and Differential Operator Extended by the Quantum Calculus |
| title_short | Multivalent Functions and Differential Operator Extended by the Quantum Calculus |
| title_sort | multivalent functions and differential operator extended by the quantum calculus |
| topic | quantum calculus analytic function subordination and superordination differential subordination univalent function open unit disk |
| url | https://www.mdpi.com/2504-3110/6/7/354 |
| work_keys_str_mv | AT samirbhadid multivalentfunctionsanddifferentialoperatorextendedbythequantumcalculus AT rabhawibrahim multivalentfunctionsanddifferentialoperatorextendedbythequantumcalculus AT shahermomani multivalentfunctionsanddifferentialoperatorextendedbythequantumcalculus |