On the Inequality Theorem for a Wider Class of Analytic Functions with Hadamard Product - Ma’moun I. Y. Alharayzeh; Maslina Darus (International Journal of Mathematics and Mathematical Sciences)
In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions f denoted by nαβ,γ which are normalized and univalent, in the unit disk D=z∈ℂ:z<1 satisfying the condition Reαz2f′′z/gz+zf′z/gz>β, 0≤α<1,0≤β<1, where g is analytic function in D, such that gz≠0, with a new condition that is introduced. The main purpose of this paper is to give an estimate for the same a3−μa22 when f belongs to the class nαβ,γ.