Certain New Class of Harmonic Functions Involving Quantum Calculus
Here in this paper, we are using the concepts of q-calculus operator theory associated with harmonic functions and define the q-Noor integral operator for harmonic functions f∈H0. We investigate a new class SH0m,q,α of harmonic functions f∈H0. In this class, we prove a necessary and sufficient convo...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6996639 |
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| author | Mohammad Faisal Khan |
| author_facet | Mohammad Faisal Khan |
| author_sort | Mohammad Faisal Khan |
| collection | DOAJ |
| description | Here in this paper, we are using the concepts of q-calculus operator theory associated with harmonic functions and define the q-Noor integral operator for harmonic functions f∈H0. We investigate a new class SH0m,q,α of harmonic functions f∈H0. In this class, we prove a necessary and sufficient convolution condition for the functions f∈H0 and also we proved that this sufficient coefficient condition is sense preserving and univalent in the class SH0m,q,α. It is proved that this coefficient condition is necessary for the functions in its subclass TSH0m,q,α. By using this necessary and sufficient coefficient condition, we obtained results based on the convexity and compactness and results on the radii of q-starlikeness and q-convexity of order α in the class TSH0m,q,α. Also we obtained extreme points for the functions in the class TSH0m,q,α. |
| format | Article |
| id | doaj-art-e3ca91e07ba04c6ba62351577337e38b |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e3ca91e07ba04c6ba62351577337e38b2025-02-03T05:53:36ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6996639Certain New Class of Harmonic Functions Involving Quantum CalculusMohammad Faisal Khan0Department of Basic ScienceHere in this paper, we are using the concepts of q-calculus operator theory associated with harmonic functions and define the q-Noor integral operator for harmonic functions f∈H0. We investigate a new class SH0m,q,α of harmonic functions f∈H0. In this class, we prove a necessary and sufficient convolution condition for the functions f∈H0 and also we proved that this sufficient coefficient condition is sense preserving and univalent in the class SH0m,q,α. It is proved that this coefficient condition is necessary for the functions in its subclass TSH0m,q,α. By using this necessary and sufficient coefficient condition, we obtained results based on the convexity and compactness and results on the radii of q-starlikeness and q-convexity of order α in the class TSH0m,q,α. Also we obtained extreme points for the functions in the class TSH0m,q,α.http://dx.doi.org/10.1155/2022/6996639 |
| spellingShingle | Mohammad Faisal Khan Certain New Class of Harmonic Functions Involving Quantum Calculus Journal of Function Spaces |
| title | Certain New Class of Harmonic Functions Involving Quantum Calculus |
| title_full | Certain New Class of Harmonic Functions Involving Quantum Calculus |
| title_fullStr | Certain New Class of Harmonic Functions Involving Quantum Calculus |
| title_full_unstemmed | Certain New Class of Harmonic Functions Involving Quantum Calculus |
| title_short | Certain New Class of Harmonic Functions Involving Quantum Calculus |
| title_sort | certain new class of harmonic functions involving quantum calculus |
| url | http://dx.doi.org/10.1155/2022/6996639 |
| work_keys_str_mv | AT mohammadfaisalkhan certainnewclassofharmonicfunctionsinvolvingquantumcalculus |