Bounds For the Coefficients of Two New Subclasses of Bi-Univalent Functions
DOI:
https://doi.org/10.25271/sjuoz.2022.10.2.922Keywords:
Taylor–Maclaurin Series, Univalent Function, Coefficient Bounds, Bi-univalent FunctionAbstract
This article discusses two new subclasses of the bi-univalent functions category ∑ in the open unit disk . The primary goal of the article is to obtain estimations of the coefficients and for the functions that are within these two new subclasses.
References
Brannan, D. A., Clunie, J., & Clunie, J. (Eds.). (1980). Aspects of contemporary complex analysis. Academic Press.
Brannan, D. A., Clunie, J., & Kirwan, W. E. (1970). Coefficient estimates for a class of star-like functions. Canadian Journal of Mathematics, 22(3), 476-485.
Brannan, D. A., & Taha, T. S. (1988). On some classes of bi-univalent functions. In Mathematical Analysis and Its Applications (pp. 53-60). Pergamon.
Breaz, D., Breaz, N., & Srivastava, H. M. (2009). An extension of the univalent condition for a family of integral operators. Applied Mathematics Letters, 22(1), 41-44.
Chichra, P. N. (1977). New subclasses of the class of close-to-convex functions. Proceedings of the American Mathematical Society, 62(1), 37-43.
Caglar, M., & Deniz, E. (2017). Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 66, 85-91.
Çağlar, M., Orhan, H., & Yağmur, N. (2013). Coefficient bounds for new subclasses of bi-univalent functions. Filomat, 27(7), 1165-1171.
Ding, S. S., Ling, Y., & Bao, G. J. (1995). Some properties of a class of analytic functions. Journal of Mathematical Analysis and applications, 195(1), 71-81.
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.
Gao, C. Y., & Zhou, S. Q. (2007). Certain subclass of starlike functions. Applied mathematics and computation, 187(1), 176-182.
Hussain, S., Khan, S., Zaighum, M. A., Darus, M., & Shareef, Z. (2017). Coefficients bounds for certain subclass of biunivalent functions associated with Ruscheweyh-Differential operator. Journal of Complex Analysis, 2017.
Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American mathematical society, 18(1), 63-68.
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.
Pommerenke, C. (1975). Univalent functions. Vandenhoeck and Ruprecht.
Ruscheweyh, S. (1975). New criteria for univalent functions. Proceedings of the American Mathematical Society, 49(1), 109-115.
Srivastava, H. M., Bulut, S., Çağlar, M., & Yağmur, N. (2013). Coefficient estimates for a general subclass of analytic and bi-univalent functions. Filomat, 27(5), 831-842.
Srivastava, H. M., & Eker, S. S. (2008). Some applications of a subordination theorem for a class of analytic functions. Applied Mathematics Letters, 21(4), 394-399.
Srivastava, H. M., Mishra, A. K., & Gochhayat, P. (2010). Certain subclasses of analytic and bi-univalent functions. Applied mathematics letters, 23(10), 1188-1192.
Styer, D., & Wright, D. J. (1981). Results on bi-univalent functions. Proceedings of the American Mathematical Society, 82(2), 243-248.
Tan, D.L.(1984). Coefficient estimates for bi-univalent functions. Chinese Ann. Math. Ser. A, 5(5), 559-568.
Xu, Q. H., Gui, Y. C., & Srivastava, H. M. (2012). Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Applied Mathematics Letters, 25(6), 990-994.
Yang, D. G., & Liu, J. L. (2010). On a class of analytic functions with missing coefficients. Applied Mathematics and Computation, 215(9), 3473-3481.
Brannan, D. A., Clunie, J., & Kirwan, W. E. (1970). Coefficient estimates for a class of star-like functions. Canadian Journal of Mathematics, 22(3), 476-485.
Brannan, D. A., & Taha, T. S. (1988). On some classes of bi-univalent functions. In Mathematical Analysis and Its Applications (pp. 53-60). Pergamon.
Breaz, D., Breaz, N., & Srivastava, H. M. (2009). An extension of the univalent condition for a family of integral operators. Applied Mathematics Letters, 22(1), 41-44.
Chichra, P. N. (1977). New subclasses of the class of close-to-convex functions. Proceedings of the American Mathematical Society, 62(1), 37-43.
Caglar, M., & Deniz, E. (2017). Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 66, 85-91.
Çağlar, M., Orhan, H., & Yağmur, N. (2013). Coefficient bounds for new subclasses of bi-univalent functions. Filomat, 27(7), 1165-1171.
Ding, S. S., Ling, Y., & Bao, G. J. (1995). Some properties of a class of analytic functions. Journal of Mathematical Analysis and applications, 195(1), 71-81.
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.
Gao, C. Y., & Zhou, S. Q. (2007). Certain subclass of starlike functions. Applied mathematics and computation, 187(1), 176-182.
Hussain, S., Khan, S., Zaighum, M. A., Darus, M., & Shareef, Z. (2017). Coefficients bounds for certain subclass of biunivalent functions associated with Ruscheweyh-Differential operator. Journal of Complex Analysis, 2017.
Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American mathematical society, 18(1), 63-68.
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.
Pommerenke, C. (1975). Univalent functions. Vandenhoeck and Ruprecht.
Ruscheweyh, S. (1975). New criteria for univalent functions. Proceedings of the American Mathematical Society, 49(1), 109-115.
Srivastava, H. M., Bulut, S., Çağlar, M., & Yağmur, N. (2013). Coefficient estimates for a general subclass of analytic and bi-univalent functions. Filomat, 27(5), 831-842.
Srivastava, H. M., & Eker, S. S. (2008). Some applications of a subordination theorem for a class of analytic functions. Applied Mathematics Letters, 21(4), 394-399.
Srivastava, H. M., Mishra, A. K., & Gochhayat, P. (2010). Certain subclasses of analytic and bi-univalent functions. Applied mathematics letters, 23(10), 1188-1192.
Styer, D., & Wright, D. J. (1981). Results on bi-univalent functions. Proceedings of the American Mathematical Society, 82(2), 243-248.
Tan, D.L.(1984). Coefficient estimates for bi-univalent functions. Chinese Ann. Math. Ser. A, 5(5), 559-568.
Xu, Q. H., Gui, Y. C., & Srivastava, H. M. (2012). Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Applied Mathematics Letters, 25(6), 990-994.
Yang, D. G., & Liu, J. L. (2010). On a class of analytic functions with missing coefficients. Applied Mathematics and Computation, 215(9), 3473-3481.
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Published
2022-06-07
How to Cite
Abdullah, khalid I., & 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
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