[1] Bieberbach L. Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Eintheitskreises vermitteln. Sitzungsber Preuss Akad Wiss Phys Math, 1916, $\mathbf{138}$: 940-955
[2] Löwner K. Untersuchungen iiber schlichte konforme Abbildungen des Einheitskreises. Math Ann, 1923, $\mathbf{89}$: 103-121
[3] Garabedian P R, Schiffer M. A proof of the Bieberbach conjecture for the fourth coefficient. J Rational Mech Anal, 1955, $\mathbf{4}$: 428-465
[4] Pederson R N, Schiffer M. A proof of the Bieberbach conjecture for the fifth coefficient. Arch Rational Mech Anal, 1972, $\mathbf{45}$: 161-193
[5] Pederson R N.A proof of the Bieberbach conjecture for the sixth coefficient. Arch Rational Mech Anal, $1968$, $\mathbf{31}$: 331-351
[6] De Branges L. A proof of the Bieberbach conjecture. Acta Math, 1985, $\mathbf{154}$(12): 137-152
[7] Brown J E, Tsao A. On the Zalcman conjecture for starlike and typically real functions. Math Z, 1986, $\mathbf{191}$: 467-474
[8] Li L, Ponnusamy S, Qiao J. Generalized Zalcman conjecture for convex functions of order $\alpha $. Acta Math Hung, 2016, $\mathbf{150}$: 234-246
[9] Ma W C. The Zalcman conjecture for close-to-convex functions. Proc Amer Math Soc, 1988, $\mathbf{104}$(3): 741-744
[10] Krushkal S L. Proof of the Zalcman conjecture for initial coefficients. Georgian Math J, 2010, $\mathbf{17}$: 663-681
[11] Krushkal S L.A short geometric proof of the Zalcman and Bieberbach conjectures. arXiv: 1408.1948
[12] Ma W. Generalized Zalcman conjecture for starlike and typically real functions. J Math Anal Appl, 1999, $\mathbf{234}$(1): 328-339
[13] Mendiratta R, Nagpal S, Ravichandran V. On a subclass of strongly starlike functions associated with exponential function. Bull Malays Math Sci Soc, 2015, $\mathbf{38}$(1): 365-386
[14] Al-Shbeil I, Faisal M I, Arif M, et al. Investigation of the Hankel determinant sharp bounds for a specific analytic function linked to a cardioid-shaped domain. Mathematics, 2023, $\mathbf{11}$(17): Article 3664
[15] Raina R K, Sharma P, Sokół J. Certain classes of analytic functions related to the crescent-shaped regions. J Contemp Math Anal, 2018, $\mathbf{53}$: 355-362
[16] Zhang H Y, Tang H, Niu X M. Third-order Hankel determinant for certain class of analytic functions related with exponential function. Symmetry, 2018, $\mathbf{10}$: Article 501
[17] Tang H, Murugusundaramoorthy G, Li S H, Ma L N. Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function. AIMS Math, 2022, $\mathbf{7}$: 6365-6380
[18] Gandhi S, Gupta P, Nagpal S, Ravichandran V. Starlike functions associated with an epicycloid. Hacet J Math Stat, 2022, $\mathbf{51}$(6): 1637-1660
[19] Pommerenke C. On the coefficients and Hankel determinants of univalent functions. J London Math Soc, 1966, $\mathbf{1}$(1): 111-122
[20] Pommerenke C. On the Hankel determinants of univalent functions. Mathematika, 1967, $\mathbf{14}$(1): 108-112
[21] Dienes P.The Taylor series: An Introduction to the Theory of Functions of a Complex Variable. New York: Dover, 1957
[22] Cantor D G. Power series with integral coefficients. Bull Am Math Soc, 1963, $\mathbf{69}$: 362-366
[23] Hasan M A, Hasan A A. Hankel matrices of finite rank with applications to signal processing and polynomials. J Math Anal Appl, 1997, $\mathbf{208}$(1): 218-242
[24] Wilson R. Determinantal criteria for meromorphic functions. Proc Lond Math Soc, 1954, $\mathbf{4}$: 357-374
[25] Faisal M I, Al-Shbeil I, Abbas M, et al. Problems concerning coefficients of symmetric starlike functions connected with the sigmoid function. Symmetry, 2023, $\mathbf{15}$(7): Article 1292
[26] Tang H, Arif M, Abbas M, et al. Analysis of coefficient-related problems for starlike functions with symmetric points connected with a three-leaf-shaped domain. Symmetry, 2023, $\mathbf{15}$(10): Article 1837
[27] Janteng A, Halim S A, Darus M. Hankel determinant for starlike and convex functions. Int J Math Anal, 2007, $\mathbf{1}$(13): 619-625
[28] Lee S K, Ravichandran V, Supramaniam S. Bounds for the second Hankel determinant of certain univalent functions. J Inequal Appl, 2013, $\mathbf{2013}$: Article 281
[29] Tang H, Ullah K, Arif M, et al. Study of second order Hankel determinants for convex functions with symmetric points related with exponential function. Journal of Innovative Research in Mathematical and Computational Sciences, 2023, $\mathbf{2}$(2): 65-108
[30] Zhang H Y, Srivastava R, Tang H. Third-order Hankel and Toeplitz determinants for starlike functions connected with the sine function. Mathematics, 2019, $\mathbf{7}$: Article 404
[31] Kowalczyk B, Lecko A, Sim Y J. The sharp bound for the Hankel determinant of the third kind for convex functions. Bull Aust Math Soc, 2018, $\mathbf{97}$: 435-445
[32] Kowalczyk B, Lecko A, Thomas D K. The sharp bound of the third Hankel determinant for starlike functions. Forum Math, 2022, $\mathbf{34}$(5): 1249-1254
[33] Kowalczyk B, Lecko A. The sharp bound of the third Hankel determinant for functions of bounded turning. Bol Soc Mat Mex, 2021, $\mathbf{27}$: Article 69
[34] Lecko A, Sim Y J, Śmiarowska B. The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2. Complex Anal Oper Theory, 2019, $\mathbf{13}$: 2231-2238
[35] Arif M, Barukab O M, Khan S A, Abbas M. The sharp bounds of Hankel determinants for the families of three-leaf-type analytic functions. Fractal Fract, 2022, $\mathbf{6}$(6): Article 291
[36] Kowalczyk B, Lecko A, Thomas D K. The sharp bound of the third Hankel determinant of convex functions of order -1/2. J Math Inequa, 2023 , $\mathbf{17}$(1): 191-204
[37] Arif M, Abbas M, Alhefthi R K, et al.Some analysis of the coefficient-related problems for functions of bounded turning associated with a symmetric image domain. Symmetry,2023, $\mathbf{15}$(11): Article 2090
[38] Banga S, Kumar S S. The sharp bounds of the second and third Hankel determinants for the class $\mathcal{S}^{\ast }$. Mathematica Slovaca, 2020, $\mathbf{70}$(4): 849-862
[39] Tang H, Arif A, Haq M, et al. Fourth hankel determinant problem based on certain analytic functions. Symmetry, 2022, $\mathbf{14}$: Article 663
[40] Kwon O S, Lecko A, Sim Y J. On the fourth coefficient of functions in the Carathéodory class. Comp Methods Funct Theory, 2018, ${\bf18}$: 307-314
[41] Ravichandran V, Verma S. Bound for the fifth coefficient of certain starlike functions. C R Math Acad Sci Paris, 2015, $\mathbf{353}$(6): 505-510
[42] Pommerenke C. Univalent Functions. Fukazawa: Tokyo Metropolitan University, 1975: 158-158
[43] Libera R J, Zlotkiewicz E J. Coefficient bounds for the inverse of a function with derivative in $\mathcal{P}$. Proc Amer Math Soc, 1983, $\mathbf{87}$(2): 251-257
