Notes on Convex Functions of Order $$\alpha $$ α

Further Properties of β-Pascu Convex Functions of Order α

The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

On the Strongly Starlikeness of Multivalently Convex Functions of Order Α

The object of the present paper is to derive some sufficient conditions for strongly starlikeness of multivalently convex functions of order α in the open unit disc. 2000 Mathematics Subject Classification. 30C45.

The norm of pre-Schwarzian derivatives on bi-univalent functions of order $alpha$

‎In the present investigation‎, ‎we give the best estimates for the norm of the pre-Schwarzian derivative $ T_{f}(z)=dfrac{f^{''}(z)}{f^{'}(z)} $ for bi-starlike functions and a new subclass of bi-univalent functions of order $ alpha $‎, ‎where‎ ‎$Vert T_{f} Vert= sup_{|z|

Mapping Properties of Hypergeometric Functions and Convolutions of Starlike or Convex Functions of Order alpha

We determine the order of convexity of hypergeometric functions z 7→ F (a, b, c, z) as well as the order of starlikeness of shifted hypergeometric functions z 7→ zF (a, b, c, z), for certain ranges of the real parameters a, b and c. As a consequence we obtain the sharp lower bound for the order of convexity of the convolution (f ∗ g)(z) := ∑∞ n=0 anbnz n when f(z) = ∑∞ n=0 anz n is convex of or...