D. Vamshee Krishna     (Department of Mathematics, Gitam School of Science, GITAM University, Visakhapatnam – 530 045, A.P., India)
D. Shalini     (Department of Mathematics, Dr. B. R. Ambedkar University, Srikakulam – 532 410, A.P., India)


In this paper, we are introducing certain subfamilies of holomorphic functions and making an attempt to obtain an upper bound (UB) to the second and third order Hankel determinants by applying certain lemmas, Toeplitz determinants, for the normalized analytic functions belong to these classes, defined on the open unit disc in the complex plane. For one of the inequality, we have obtained sharp bound.


Holomorphic function, upper bound, Hankel determinant, positive real function.

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DOI: http://dx.doi.org/10.15826/umj.2022.1.011

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