New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality
In the recent past, various new subclasses of normalized harmonic functions have been defined in open unit disk U which satisfy second-order and third-order differential inequalities. Here, in this study, we define a new class of normalized harmonic functions in open unit disk U which is satisfying...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4051867 |
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| author | Mohammad Faisal Khan Khaled Matarneh Shahid Khan Saqib Hussain Maslina Darus |
| author_facet | Mohammad Faisal Khan Khaled Matarneh Shahid Khan Saqib Hussain Maslina Darus |
| author_sort | Mohammad Faisal Khan |
| collection | DOAJ |
| description | In the recent past, various new subclasses of normalized harmonic functions have been defined in open unit disk U which satisfy second-order and third-order differential inequalities. Here, in this study, we define a new class of normalized harmonic functions in open unit disk U which is satisfying a fourth-order differential inequality. We investigate some useful results such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution for the functions belonging to this new class of harmonic functions. In addition, under convex combination and convolution of its members, we prove that this new class is closed, and we also give some lemmas to prove our main results. |
| format | Article |
| id | doaj-art-2e7a0e95c62a427a8d0d5760865aff32 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2e7a0e95c62a427a8d0d5760865aff322025-02-03T05:57:22ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4051867New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential InequalityMohammad Faisal Khan0Khaled Matarneh1Shahid Khan2Saqib Hussain3Maslina Darus4Department of Basic ScienceFaculty of Computer ScienceDepartment of MathematicsDepartment of MathematicsDepartment of Mathematical SciencesIn the recent past, various new subclasses of normalized harmonic functions have been defined in open unit disk U which satisfy second-order and third-order differential inequalities. Here, in this study, we define a new class of normalized harmonic functions in open unit disk U which is satisfying a fourth-order differential inequality. We investigate some useful results such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution for the functions belonging to this new class of harmonic functions. In addition, under convex combination and convolution of its members, we prove that this new class is closed, and we also give some lemmas to prove our main results.http://dx.doi.org/10.1155/2022/4051867 |
| spellingShingle | Mohammad Faisal Khan Khaled Matarneh Shahid Khan Saqib Hussain Maslina Darus New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality Journal of Mathematics |
| title | New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality |
| title_full | New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality |
| title_fullStr | New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality |
| title_full_unstemmed | New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality |
| title_short | New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality |
| title_sort | new class of close to convex harmonic functions defined by a fourth order differential inequality |
| url | http://dx.doi.org/10.1155/2022/4051867 |
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