Third Hankel determinants for two classes of analytic functions with real coefficients
-
Young Jae Sim
und
Paweł Zaprawa
Abstract
In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of
Funding source: Ministerstwo Nauki i Szkolnictwa Wyższego
Award Identifier / Grant number: 030/RID/2018/19
Funding statement: The project/research was financed in the framework of the project Lublin University of Technology – Regional Excellence Initiative, funded by the Polish Ministry of Science and Higher Education (contract no. 030/RID/2018/19).
References
[1]
A. A. Amourah, F. Yousef, T. Al-Hawary and M. Darus,
On
[2] D. Bansal, S. Maharana and J. K. Prajapat, Third order Hankel determinant for certain univalent functions, J. Korean Math. Soc. 52 (2015), no. 6, 1139–1148. 10.4134/JKMS.2015.52.6.1139Suche in Google Scholar
[3] R. Bucur, D. Breaz and L. Georgescu, Third Hankel determinant for a class of analytic functions with respect to symmetric points, Acta Univ. Apulensis Math. Inform. 42 (2015), 79–86. 10.17114/j.aua.2015.42.06Suche in Google Scholar
[4] P. L. Duren, Univalent Functions, Springer, New York, 1983. Suche in Google Scholar
[5] B. Kowalczyk, A. Lecko, M. Lecko and Y. J. Sim, The sharp bound of the third Hankel determinant for some classes of analytic functions, Bull. Korean Math. Soc. 55 (2018), no. 6, 1859–1868. Suche in Google Scholar
[6] B. A. Kowalczyk, A. Lecko and Y. J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc. 97 (2018), no. 3, 435–445. 10.1017/S0004972717001125Suche in Google Scholar
[7] O. S. Kwon, A. Lecko and Y. J. Sim, On the fourth coefficient of functions in the Carathéodory class, Comput. Methods Funct. Theory 18 (2018), no. 2, 307–314. 10.1007/s40315-017-0229-8Suche in Google Scholar
[8] O. S. Kwon, A. Lecko and Y. J. Sim, The bound of the Hankel determinant of the third kind for starlike functions, Bull. Malays. Math. Sci. Soc. 42 (2019), no. 2, 767–780. 10.1007/s40840-018-0683-0Suche in Google Scholar
[9] O. S. Kwon and Y. J. Sim, The sharp bound of the Hankel determinant of the third kind for starlike functions with real coefficients, Mathematics 7 (2019), 10.3390/math7080721. 10.3390/math7080721Suche in Google Scholar
[10] A. Lecko, Y. J. Sim and B. Śmiarowska, The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2, Complex Anal. Oper. Theory 13 (2019), no. 5, 2231–2238. 10.1007/s11785-018-0819-0Suche in Google Scholar
[11]
M. Obradović and N. Tuneski,
Some properties of the class
[12] M. Raza and S. N. Malik, Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, J. Inequal. Appl. 2013 (2013), Article ID 412. 10.1186/1029-242X-2013-412Suche in Google Scholar
[13] M. S. Robertson, On the coefficients of a typically-real function, Bull. Amer. Math. Soc. 41 (1935), no. 8, 565–572. 10.1090/S0002-9904-1935-06147-6Suche in Google Scholar
[14] D. Vamshee Krishna, B. Venkateswarlu and T. RamReddy, Third Hankel determinant for certain subclass of p-valent functions, Complex Var. Elliptic Equ. 60 (2015), no. 9, 1301–1307. 10.1080/17476933.2015.1012162Suche in Google Scholar
[15] P. Zaprawa, Second Hankel determinants for the class of typically real functions, Abstr. Appl. Anal. 2016 (2016), Article ID 3792367. 10.1155/2016/3792367Suche in Google Scholar
[16] P. Zaprawa, P. Hankel determinants for univalent functions related to the exponential function, Symmetry 11 (2019), no. 10, 10.3390/sym11101211. 10.3390/sym11101211Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Higher depth mock theta functions and q-hypergeometric series
- Topological and algebraic properties of universal groups for right-angled buildings
- On the socles of characteristically inert subgroups of Abelian p-groups
- Priestley duality for MV-algebras and beyond
- The cardinality of μM,D‐orthogonal exponentials for the planar four digits
- Associated prime ideals of equivariant coinvariant algebras, Steenrod operations, and Krull’s Going Down Theorem
- Ordered fields dense in their real closure and definable convex valuations
- Third Hankel determinants for two classes of analytic functions with real coefficients
- A common range problem for model spaces
- Generalized Ricci flow on nilpotent Lie groups
- Endpoint estimates for a trilinear pseudo-differential operator with flag symbols
- The role of the algebraic structure in Wold-type decomposition
- Incidences between Euclidean spaces over finite fields
- Cancellation in algebraic twisted sums on GL_m
Artikel in diesem Heft
- Frontmatter
- Higher depth mock theta functions and q-hypergeometric series
- Topological and algebraic properties of universal groups for right-angled buildings
- On the socles of characteristically inert subgroups of Abelian p-groups
- Priestley duality for MV-algebras and beyond
- The cardinality of μM,D‐orthogonal exponentials for the planar four digits
- Associated prime ideals of equivariant coinvariant algebras, Steenrod operations, and Krull’s Going Down Theorem
- Ordered fields dense in their real closure and definable convex valuations
- Third Hankel determinants for two classes of analytic functions with real coefficients
- A common range problem for model spaces
- Generalized Ricci flow on nilpotent Lie groups
- Endpoint estimates for a trilinear pseudo-differential operator with flag symbols
- The role of the algebraic structure in Wold-type decomposition
- Incidences between Euclidean spaces over finite fields
- Cancellation in algebraic twisted sums on GL_m
