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The class of functions defined using linear combination of the derivatives of ratio of the normalized analytic function with the identity function is considered in this manuscript. Further, the sharp bounds on the Hankel determinants and estimates on the higher order Schwarzian derivatives for the first three consecutive derivatives are investigated. [ABSTRACT FROM AUTHOR]

The class B¯ B(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯ B(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + … ∊ B¯(α) are investigated. Further sharp estimate on the functional ®a2a3 - a4® is also obtained. [ABSTRACT FROM AUTHOR]

The class B¯(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + ... ∊ B¯(α) are investigated. Further sharp estimate on the functional ∣a2a3 - a4∣ is also obtained. [ABSTRACT FROM AUTHOR]

The class B¯(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + ... ∊ B¯(α) are investigated. Further sharp estimate on the functional ∣a2a3 - a4∣ is also obtained. [ABSTRACT FROM AUTHOR]

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients. [ABSTRACT FROM AUTHOR]