Second Hankel determinant for a class of bi-univalent functions defined on a leaf-like domain
DOI:
https://doi.org/10.5269/bspm.83310Resumen
In this paper, a new subclass $\mathfrak{B}\mathfrak{K}(u,v,\phi)$ of bi-univalent function is introduced in related with a leaf-like domain. The initial coefficients and an upper bound for the second Hankel determinant for functions belonging to this class has been investigated. The obtained results are validated through numerical illustrations and are shown to generalize and improve several known results in the existing literature.
Furthermore, we investigate the structural properties of this subclass and highlight its potential significance in real-world applications, particularly in areas involving geometric function theory and related analytical models.
Referencias
{\em Functions which map the interior of the unit circle upon simple regions}, Ann. Math. 17, no. 1, 12--22, (1915).
\bibitem{ay16} Altinkaya, S. and Ya\c{c}in, S.,
{\em Upper bound of second Hankel determinant for bi-Bazilevi\v{c} functions}, Mediterr. J. Math. 13, no. 6, 4081--4090, (2016).
\bibitem{b13} Bulut, S.,
{\em Coefficient estimates for a class of analytic and bi-univalent functions}, Novi Sad J. Math. 43, no. 2, 59--65, (2013).
\bibitem{cds17} \c{C}a\u{g}ler, M., Deniz, E. and Srivastava, H. M.,
{\em Second Hankel determinant for certain subclasses of bi-univalent functions}, Turkish J. Math. 41, no. 3, 694--706, (2017).
\bibitem{coy13} \c{C}a\u{g}ler, M., Orhan, H. and Ya\u{g}mur, N.,
{\em Coefficient bounds for new subclasses of bi-univalent functions}, Filomat 27, no. 7, 1165--1171, (2013).
\bibitem{dco15} Deniz, E., \c{C}a\u{g}ler, M. and Orhan, H.,
{\em Second Hankel determinant for bi-starlike and bi-convex functions of order $\beta$}, Appl. Math. Comput. 271, 301--307, (2015).
\bibitem{fr10} Frasin, B. A.,
{\em Coefficient inequalities for certain classes of Sakaguchi type functions}, Int. J. Nonlinear Sci. 10, 206--211, (2010).
\bibitem{gs58} Grenander, U. and Szeg\"o, G.,
{\em Toeplitz forms and their applications}, California Monographs in Mathematical Sciences, Univ. California Press, Berkeley, (1958).
\bibitem{gc22} Singh, G. and Kaur, C.,
{\em Fekete--Szeg\"o inequality for analytic functions with (p,q)-derivative operator subordinate to leaf-like domain}, (2022).
\bibitem{omb} Orhan, H., Magesh, N. and Balaji, V. K.,
{\em Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials}, Asian-Eur. J. Math. 12, no. 2, 1950017, (2019).
\bibitem{owa7} Owa, S., Sekine, T. and Yamakawa, R.,
{\em On Sakaguchi type functions}, Appl. Math. Comput. 187, 356--361, (2007).
\bibitem{p75} Pommerenke, C.,
{\em Univalent functions}, Vandenhoeck and Ruprecht, G\"ottingen, (1975).
\bibitem{ro36} Robertson, M. S.,
{\em On the theory of univalent functions}, Ann. Math. 37, no. 2, 374--408, (1936).
\bibitem{sa59} Sakaguchi, K.,
{\em On a certain univalent mapping}, J. Math. Soc. Japan 11, no. 1, 72--75, (1959).
\bibitem{sri10} Srivastava, H. M., Mishra, A. K. and Gochhayat, P.,
{\em Certain subclasses of analytic and bi-univalent functions}, Appl. Math. Lett. 23, 1188--1192, (2010).
\bibitem{vd99} Vein, R. and Dale, P.,
{\em Determinants and their applications in mathematical physics}, Applied Mathematical Sciences 134, Springer, New York, (1999).
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\bibitem{br15} Bansal, D. and Prajapat, J. K.,
{\em Certain geometric properties of analytic and bi-univalent functions}, J. Egyptian Math. Soc. 24, no. 2, 304--308, (2016).
\bibitem{mur16} Murugusundaramoorthy, S. and Vijaya, K.,
{\em Coefficient estimates of certain subclasses of bi-univalent functions associated with Hohlov operator}, Global J. Pure Appl. Math. 12, 3185--3196, (2016).
\bibitem{abd20} Amourah, A. A. and Yousef, F.,
{\em Coefficient estimates for new subclasses of analytic and bi-univalent functions associated with a generalized operator}, Symmetry 12, 1--12, (2020).
\bibitem{ravi21} Ravichandran, K. S., Gangadharan, A. and Darus, M.,
{\em Fekete--Szeg\"o problem for certain subclasses of analytic and bi-univalent functions}, Mathematics 9, 1--12, (2021).
\bibitem{tah18} Bulboac\u{a}, T. and Murugusundaramoorthy, G.,
{\em Second Hankel determinant for subclasses of analytic and bi-univalent functions defined by convolution}, Math. Moravica 22, 1--12, (2018).
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