Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions of Bounded Turning Associated with Petal-Shaped Domain

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Sharp estimate of logarithmic coefficients of certain class of analytic functions

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Extremal Bounds for Functions of Bounded Turning

In this article, we determined the upper and lower bounds for functions having the properties of bounded turning by using the convexity techniques. Moreover, the bounds of the partial sums are estimated near the origin. 1 Introduction Let H be the class of functions analytic in the open unit disk U = {z : z ∈ C, |z| < 1} and H[a, n] be the subclass of H consisting of functions of the form f (z)...

Bounds of Hankel Determinant for a Class of Univalent Functions

Bounds for the second Hankel determinant of certain univalent functions

*Correspondence: [email protected] 1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia Full list of author information is available at the end of the article Abstract The estimates for the second Hankel determinant a2a4 – a3 of the analytic function f (z) = z + a2z + a3z + · · · , for which either zf ′(z)/f (z) or 1 + zf ′′(z)/f ′(z) is subordinate to a certai...