OEFFICIENT ESTIMATES OF NEW SPECIAL SUBCATEGORY OF BI-UNIVALENT FUNCTIONS
DOI:
https://doi.org/10.25271/sjuoz.2024.12.4.1307Keywords:
Analytic Function, Bi-univalent Function, q-derivative, SubordinationAbstract
In the present paper, we introduce and investigate a new subcategory H_Σ (q,β;ς) of analytic and bi-univalent functions in the open unit disk D based on the ideas of q-derivative operator and subordination. For the functions belong to the subcategory H_Σ (q,β;ς) , upper bounds for the second and third coefficients are found and some special outcomes of the main result are also presented.
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Alimohammadi, D., Cho, N. E., Adegani, E. A., & Motamednezhad, A. (2020). Argument and coefficient estimates for certain analytic functions. Mathematics, 8(1), 88. https://doi.org/10.3390/math8010088.
Alrefai, O., & Ali, M. (2020). General coefficient estimates for bi-univalent functions: a new approach. Turkish Journal of Mathematics, 44(1), 240-251. 10.3906/mat-1910-100.
Brannan, D. A., & Clunie, J. (1980). Aspects of contemporary complex analysis. (No Title).
Duren, P. L. (1983). Grundlehren der Mathematischen Wissenchaffen. Univalent Functions; Springer: New York, NY, USA; Berlin/Heidelberg, Germany, 259.
Duren, P. L. (2001). Univalent functions (Vol. 259). Springer Science & Business Media.
Frasin, B. A., & Aouf, M. K. (2011). New subclasses of bi-univalent functions. Applied Mathematics Letters, 24(9), 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048.
Jackson, F. H. (1909). XI.—On q-functions and a certain difference operator. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 46(2), 253-281. https://doi.org/10.1017/S0080456800002751.
Jackson, F. H. (1910). On q-definite integrals. Quart. J. Pure Appl. Math, 41(15), 193-203.
Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American mathematical society, 18(1), 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1.
Ma, W. (1992). A unified treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis, 1992. International Press Inc.
Hameed Mohammed, N. H. (2021). Coefficient Bounds for a New Class of Bi-Univalent Functions Associated with Subordination. Mathematical Analysis and Convex Optimization, 2(2), 73-82. 10.52547/maco.2.2.8.
Mohammed, N. H. (2022). Bounds for the coefficients of two new subclasses of bi-univalent functions. Science Journal of University of Zakho, 10(2), 66-69. https://doi.org/10.25271/sjuoz.2022.10.2.922.
Mohammed, N. H., Adegani, E. A., Bulboacă, T. E. O. D. O. R., & Cho, N. E. (2022). A family of holomorphic functions defined by differential inequality. Math. Inequal. Appl, 25, 27-39. http://dx.doi.org/10.7153/mia-2022-25-03.
Netanyahu, E. (1969). The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1. Archive for rational mechanics and analysis, 32(2), 100-112. 10.1007/BF00247676.
Saravanan, G., & Muthunagai, K. (2019). Coefficient bounds for a new subclass of bi-univalent functions defined by q-fractional derivative operator. Recent Developments in Mathematical Analysis and Computing, 2095(1), 030023. 10.1063/1.5097534.
Seoudy, T. M., & Aouf, M. K. (2014). Convolution Properties for Certain Classes of Analytic Functions Defined by q‐Derivative Operator. In Abstract and Applied Analysis (Vol. 2014, No. 1, p. 846719). Hindawi Publishing Corporation. https://doi.org/10.1155/2014/846719.
Srivastava, H. M. (1989). Univalent functions, fractional calculus, and associated generalized hypergeometric functions. Univalent Functions, Fractional Calculus, and Their Applications; Srivastava, HM, Owa, S., Eds, 329-354.
Srivastava, H. M., & Owa, S. (1992). Current topics in analytic function theory. World Scientific.
Toklu, E. (2019). A new subclass of bi-univalent functions defined by q-derivative. TWMS Journal of Applied and Engineering Mathematics, 9(1), 84-90.
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Copyright (c) 2024 Kosrat O. Mohammed, Khalid I. Abdullah, Nafya H. Mohammed, Abubakr M. Adarbar, Hedayat M. Sharifi

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