Certain coefficient inequalities associated with Hankel determinant for a specific subfamily of holomorphic mappings

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.

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...

Second Hankel Determinant for Certain Classes of Analytic Functions

G. Shanmugam, Research Scholar, Department of Mathematics, Madras Christian College, Tambaram, Tamil Nadu, India. E-mail: [email protected] B. Adolf Stephen, Associate Professor, Department of Mathematics, Madras Christian College, Tambaram, Tamil Nadu, India. E-mail: [email protected] K. G. Subramanian, Professor, School of Computer Sciences, Universiti Sains Malaysia, 11800 USM, ...

Coefficient Inequalities for Certain Analytic Functions

Coefficient Inequalities for Certain Classes of Sakaguchi Type Functions

for complex numbers s, t with s ∕= t and for α(0 ≤ α < 1). Sufficient condition involving coefficient inequalities for f(z) to in the class S(α, t) and T (α, s, t) are obtained, where f(z) ∈ T (α, s, t) if and only if zf ′(z) ∈ S(α, s, t). Our main result contain some interesting corollaries (known or new) as special cases.