Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving q-Chebyshev Polynomials
In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new...
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| Published in | Journal of mathematics (Hidawi) Vol. 2022; no. 1 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo
Hindawi
2022
John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new subclass of analytic and bi-univalent functions. For this newly defined functions’ classes, a number of coefficient bounds, along with the Fekete–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks. |
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| AbstractList | In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new subclass of analytic and bi-univalent functions. For this newly defined functions’ classes, a number of coefficient bounds, along with the Fekete–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks. In recent years, the usage of the q ‐derivative and symmetric q ‐derivative operators is significant. In this study, firstly, many known concepts of the q ‐derivative operator are highlighted and given. We then use the symmetric q ‐derivative operator and certain q ‐Chebyshev polynomials to define a new subclass of analytic and bi‐univalent functions. For this newly defined functions’ classes, a number of coefficient bounds, along with the Fekete–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks. |
| Author | Araci, Serkan Liu, Zhi-Guo Khan, Muhammad Ghaffar Khan, Bilal Shaba, Timilehin Gideon Khan, Nazar |
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| Cites_doi | 10.1090/s0002-9939-1967-0206255-1 10.3390/math8101676 10.1007/s40995-019-00815-0 10.3390/sym13071275 10.3390/sym12020291 10.2140/pjm.1983.104.269 10.1007/bf00247676 10.1112/jlms/s1-8.2.85 10.3390/sym13101840 |
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| Copyright | Copyright © 2022 Bilal Khan et al. Copyright © 2022 Bilal Khan et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | e_1_2_8_17_2 e_1_2_8_12_2 e_1_2_8_13_2 Khan B. (e_1_2_8_6_2) 2021; 15 e_1_2_8_14_2 e_1_2_8_15_2 Srivastava H. M. (e_1_2_8_8_2) 1989 e_1_2_8_9_2 e_1_2_8_2_2 Jackson F. H. (e_1_2_8_5_2) 1910; 41 e_1_2_8_1_2 e_1_2_8_3_2 e_1_2_8_10_2 Brannan D. A. (e_1_2_8_4_2) 1986; 31 e_1_2_8_11_2 Khan B. (e_1_2_8_7_2) 2021; 440 Duren P. L. (e_1_2_8_16_2) 1983 Altinkaya S. (e_1_2_8_18_2) 2017; 4 |
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| Title | Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving q-Chebyshev Polynomials |
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