[1] |
Chichra, P. N., New subclasses of the class of close-to-convex functions, Proc. Am. Math. Soc., 1, 62, 37-43, 1977 · Zbl 0355.30013 · doi:10.1090/S0002-9939-1977-0425097-1 |
[2] |
Singh, R.; Singh, S., Convolution properties of a class of starlike functions, Proc. Am. Math. Soc., 106, 1, 145-152, 1989 · Zbl 0672.30007 · doi:10.1090/S0002-9939-1989-0994388-6 |
[3] |
Krzyz, J.: A counter example concerning univalent functions. Mat. Fiz. Chem., 57-58 (1962) |
[4] |
Noor, K. I.; Khan, N., Some convolution properties of a subclass of p-valent functions, Maejo Int. J. Sci. Technol., 9, 2, 181-192, 2015 |
[5] |
Khan, N.; Khan, B.; Ahmad, Q. Z.; Ahmad, S., Some convolution properties of multivalent analytic functions, AIMS Math., 2, 2, 260-268, 2017 · Zbl 1431.30016 · doi:10.3934/Math.2017.2.260 |
[6] |
Miller, S. S., Differential inequalities and Carathéodory functions, Bull. Am. Math. Soc., 81, 79-81, 1975 · Zbl 0302.30003 · doi:10.1090/S0002-9904-1975-13643-3 |
[7] |
Bieberbach, L., Über die koeffizienten derjenigen potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitz.ber. Preuss. Akad. Wiss., 138, 940-955, 1916 · JFM 46.0552.01 |
[8] |
De Branges, L., A proof of the Bieberbach conjecture, Acta Math., 154, 137-152, 1985 · Zbl 0573.30014 · doi:10.1007/BF02392821 |
[9] |
Ma, W. C.; Minda, D.; Li, Z.; Ren, F.; Yang, L.; Zhang, S., A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis, 157-169, 1994, Cambridge: International Press, Cambridge · Zbl 0823.30007 |
[10] |
Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Pol. Math., 23, 159-177, 1970 · Zbl 0199.39901 · doi:10.4064/ap-23-2-159-177 |
[11] |
Sokół, J.; Stankiewicz, J., Radius of convexity of some subclasses of strongly starlike functions, Zesz. Nauk. Politech. Rzesz., Mat. Fiz., 19, 101-105, 1996 · Zbl 0880.30014 |
[12] |
Arif, M.; Raza, M.; Tang, H.; Hussain, S.; Khan, H., Hankel determinant of order three for familiar subsets of analytic functions related with sine function, Open Math., 17, 1615-1630, 2019 · Zbl 1441.30019 · doi:10.1515/math-2019-0132 |
[13] |
Alahmade, A.; Mujahid, Z.; Tawfiq, F. M.O.; Khan, B.; Khan, N.; Tchier, F., Third Hankel determinant for subclasses of analytic and m-fold symmetric functions involving cardioid domain and sine function, Symmetry, 2023, 2039 |
[14] |
Sharma, K.; Jain, N. K.; Ravichandran, V., Starlike functions associated with cardioid, Afr. Math., 27, 923-939, 2016 · Zbl 1352.30015 · doi:10.1007/s13370-015-0387-7 |
[15] |
Mendiratta, R.; Nagpal, S.; Ravichandran, V., On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., 38, 365-386, 2015 · Zbl 1312.30019 · doi:10.1007/s40840-014-0026-8 |
[16] |
Srivastava, H. M.; Khan, B.; Khan, N.; Tahir, M.; Ahmad, S.; Khan, N., Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function, Bull. Sci. Math., 167, 2021 · Zbl 1459.05020 · doi:10.1016/j.bulsci.2020.102942 |
[17] |
Pommerenke, C.: On the coefficients and Hankel determinants of univalent functions. J. Lond. Math. Soc., 111-122 (1966) · Zbl 0138.29801 |
[18] |
Noonan, J.W., Thomas, D.K.: On second Hankel determinant of a really mean p-valent functions. Trans. Am. Math. Soc., 337-346 (1976) · Zbl 0346.30012 |
[19] |
Karthikeyan, K.R., Murugusundaramoorthy, G., Purohit, S.D., Suthar, D.L.: Certain class of analytic functions with respect to symmetric points defined by q-calculus. J. Math. (2021) · Zbl 1477.30011 |
[20] |
Janteng, A.; Halim, A. S.; Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal., 1, 619-625, 2007 · Zbl 1137.30308 |
[21] |
Obradović, M.; Tuneski, N., Hankel determinants of second and third order for the class S of univalent functions, Math. Slovaca, 71, 649-654, 2021 · Zbl 1482.30048 · doi:10.1515/ms-2021-0010 |
[22] |
Cho, N. E.; Kowalczyk, B.; Kwon, O. S.; Lecko, A.; Sim, Y. J., Some coefficient inequalities related to the Hankel determinant for strongly starlike functions of order alpha, J. Math. Inequal., 11, 429-439, 2017 · Zbl 1369.30015 · doi:10.7153/jmi-11-36 |
[23] |
Cho, N. E.; Kowalczyk, B.; Kwon, O. S.; Lecko, A.; Sim, Y. J., The bounds of some determinants for starlike functions of order alpha, Bull. Malays. Math. Sci. Soc., 41, 523-535, 2018 · Zbl 1387.30007 · doi:10.1007/s40840-017-0476-x |
[24] |
Babalola, K. O., On \(H_3(1)\) Hankel determinant for some classes of univalent functions, Inequal. Theory Appl., 6, 1-7, 2010 |
[25] |
Srivastava, H. M.; Rath, B.; Kumar, K. S.; Krishna, D. V., Some sharp bounds of the third-order Hankel determinant for the inverses of the Ozaki type close-to-convex functions, Bull. Sci. Math., 191, 1-9, 2024 · Zbl 1535.30045 · doi:10.1016/j.bulsci.2023.103381 |
[26] |
Srivastava, H. M.; Alshammari, K.; Darus, M., A new \(q\)-fractional integral operator and its applications to the coefficient problem involving the second Hankel determinant for q-starlike and q-convex functions, J. Nonlinear Var. Anal., 7, 985-994, 2023 · Zbl 07788154 |
[27] |
Shi, L.; Arif, M.; Srivastava, H. M.; Ihsan, M., Sharp bounds on the Hankel determinant of the inverse functions for certain analytic functions, J. Math. Inequal., 17, 1129-1143, 2023 · Zbl 1526.30024 · doi:10.7153/jmi-2023-17-73 |
[28] |
Srivastava, H. M.; Shaba, T. G.; Murugusundaramoorthy, G.; Wanas, A. K.; Oros, G. I., The Fekete-Szegŏ functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator, AIMS Math., 8, 340-360, 2022 · doi:10.3934/math.2023016 |
[29] |
Zaprawa, P., Third Hankel determinants for subclasses of univalent functions, Mediterr. J. Math., 14, 2017 · Zbl 1362.30027 · doi:10.1007/s00009-016-0829-y |
[30] |
Kwon, O. S.; Lecko, A.; Sim, Y. J., The bound of the Hankel determinant of the third kind for starlike functions, Bull. Malays. Math. Sci. Soc., 42, 767-780, 2019 · Zbl 1419.30007 · doi:10.1007/s40840-018-0683-0 |
[31] |
Zaprawa, P.; Obradovic, M.; Tuneski, N., Third Hankel determinant for univalent starlike functions, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., 115, 2021 · Zbl 1461.30048 · doi:10.1007/s13398-020-00977-2 |
[32] |
Sim, Y. J.; Lecko, A.; Thomas, D. K., The second Hankel determinant for strongly convex and Ozaki close-to-convex functions, Ann. Mat. Pura Appl., 200, 2515-2533, 2021 · Zbl 1476.30074 · doi:10.1007/s10231-021-01089-3 |
[33] |
Srivastava, H. M.; Ahmad, Q. Z.; Khan, N.; Khan, N.; Khan, B., Hankel Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain, Mathematics, 7, 2019 · doi:10.3390/math7020181 |
[34] |
Srivastava, H. M.; Kaur, G.; Singh, G., Estimates of the fourth Hankel determinant for a class of analytic functions with bounded turnings involving cardioid domains, J. Nonlinear Convex Anal., 22, 511-526, 2021 · Zbl 1498.30014 |
[35] |
Breaz, D.; Khan, S.; Tawfiq, F. M.O.; Tchier, F., Applications of fuzzy differential subordination to the subclass of analytic functions involving Riemann-Liouville fractional integral operator, Mathematics, 11, 2023 · doi:10.3390/math11244975 |
[36] |
Tang, H.; Srivastava, H. M.; Li, H.-S.; Deng, G.-T., Correction to majorization results for break subclasses of starlike functions based on the sine and cosine functions, Bull. Iran. Math. Soc., 46, 389-391, 2020 · Zbl 1435.30067 · doi:10.1007/s41980-019-00291-7 |
[37] |
Shi, L.; Srivastava, H. M.; Rafiq, R.; Arif, M.; Ihsan, M., Results on Hankel determinants for the inverse of certain analytic functions subordinated to the exponential function, Mathematics, 10, 1-15, 2022 · doi:10.3390/math10193429 |
[38] |
Srivastava, H. M.; Kumar, S.; Kumar, V.; Cho, N. E., Hermitian-Toeplitz and Hankel determinants for starlike functions associated with a rational function, J. Nonlinear Convex Anal., 23, 2815-2833, 2022 · Zbl 1499.30172 |
[39] |
Srivastava, H. M.; Kaur, G.; Singh, G., Estimates of the fourth Hankel determinant for a class of analytic functions with bounded turnings involving cardioid domains, J. Nonlinear Convex Anal., 22, 511-526, 2021 · Zbl 1498.30014 |
[40] |
Srivastava, H. M.; Khan, B.; Khan, N.; Tahir, M.; Ahmad, S.; Khan, N., Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function, Bull. Sci. Math., 167, 1-16, 2021 · Zbl 1459.05020 · doi:10.1016/j.bulsci.2020.102942 |
[41] |
Joseph, O. A.F.; Kadir, B. B.; Akinwumi, S. E.; Adeniron, E. O., Polynomial bounds for a class of univalent functions involving sigmoid function, Khayyam J. Math., 4, 88-101, 2018 · Zbl 1412.30038 |
[42] |
Swamy, S. R.; Bulut, S.; Sailaja, R., Some special families of holomorphic and Sălăgean type bi-univalent functions associated with Horadam polynomials involving a modified sigmoid activation function, Hacet. J. Math. Stat., 50, 710-720, 2021 · Zbl 1488.30133 · doi:10.15672/hujms.695858 |
[43] |
Sãlaãgean, G. S., Subclasses of univalent functions, Complex Analysis, Fifth Romanian-Finnish Seminar, Part 1, 362-372, 1983, Berlin: Springer, Berlin · Zbl 0531.30009 · doi:10.1007/BFb0066543 |
[44] |
Khan, M. G.; Ahmad, B.; Sokol, J.; Muhammad, Z.; Mashwani, W. K.; Chinram, R.; Petchkaew, P., Coefficient problems in a class of functions with bounded turning associated with sine function, Eur. J. Pure Appl. Math., 14, 1, 53-64, 2021 · doi:10.29020/nybg.ejpam.v14i1.3902 |
[45] |
Pommerenke, C., Univalent Functions, 1975, Gottingen: Vandenhoeck & Ruprecht, Gottingen · Zbl 0188.38303 |
[46] |
Keough, F.; Merkes, E., A coefficient inequality for certain subclasses of analytic functions, Proc. Am. Math. Soc., 20, 8-12, 1969 · Zbl 0165.09102 · doi:10.1090/S0002-9939-1969-0232926-9 |
[47] |
Arif, M.; Raza, M.; Tang, H.; Hussain, S.; Khan, H., Hankel determinant of order three for familiar subsets of analytic functions related with sine function, Open Math., 17, 1615-1630, 2019 · Zbl 1441.30019 · doi:10.1515/math-2019-0132 |
[48] |
Libera, R. J.; Zlotkiewiez, E. J., Early coefficient of the inverse of a regular convex function, Proc. Am. Math. Soc., 85, 225-230, 1982 · Zbl 0464.30019 · doi:10.1090/S0002-9939-1982-0652447-5 |
[49] |
Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 1983, New York: Springer, New York · Zbl 0514.30001 |
[50] |
Ravichandran, V.; Verma, S., Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci., 353, 505-510, 2015 · Zbl 1317.30022 · doi:10.1016/j.crma.2015.03.003 |