Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series
In this paper, we define a new class $ \mathcal{R}_{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $ of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janow...
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AIMS Press
2024-10-01
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| author | Kholood M. Alsager Sheza M. El-Deeb Ala Amourah Jongsuk Ro |
| author_facet | Kholood M. Alsager Sheza M. El-Deeb Ala Amourah Jongsuk Ro |
| author_sort | Kholood M. Alsager |
| collection | DOAJ |
| description | In this paper, we define a new class $ \mathcal{R}_{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $ of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function $ \mathcal{G}^{-1} $ when $ \mathcal{G}\in \mathcal{R} _{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $. Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions. |
| format | Article |
| id | doaj-art-f531699021024a9da3408e94b8317b13 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-f531699021024a9da3408e94b8317b132025-08-20T02:18:47ZengAIMS PressAIMS Mathematics2473-69882024-10-01910293702938510.3934/math.20241423Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial seriesKholood M. Alsager 0Sheza M. El-Deeb 1Ala Amourah 2Jongsuk Ro 31. Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia1. Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia2. Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman 3. Jadara Research Center, Jadara University, Irbid 21110, Jordan4. School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea 5. Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of KoreaIn this paper, we define a new class $ \mathcal{R}_{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $ of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function $ \mathcal{G}^{-1} $ when $ \mathcal{G}\in \mathcal{R} _{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $. Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions.https://www.aimspress.com/article/doi/10.3934/math.20241423?viewType=HTMLholomorphic functionsconvolutionstarlike and convex functionsfekete-szegöfunctionalsubordinationbinomial seriesbabalola operatorjanowski function |
| spellingShingle | Kholood M. Alsager Sheza M. El-Deeb Ala Amourah Jongsuk Ro Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series AIMS Mathematics holomorphic functions convolution starlike and convex functions fekete-szegöfunctional subordination binomial series babalola operator janowski function |
| title | Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series |
| title_full | Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series |
| title_fullStr | Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series |
| title_full_unstemmed | Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series |
| title_short | Some results for the family of holomorphic functions associated with the Babalola operator and combination binomial series |
| title_sort | some results for the family of holomorphic functions associated with the babalola operator and combination binomial series |
| topic | holomorphic functions convolution starlike and convex functions fekete-szegöfunctional subordination binomial series babalola operator janowski function |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241423?viewType=HTML |
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