Extensions of some generalized conditions for starlikeness and convexity

Some Sufficient Conditions for Starlikeness and Convexity of Order α

Some Sufficient Conditions for Univalence and Starlikeness

The object of the present paper is to derive certain sufficient conditions for univalence, p-valently starlikeness and p-valently close-to-convexity of analytic functions in the unit disk. Our results extend and improve some results due to Owa [3], Frasin and Darus [2] and Chen [1].

Some Sufficient Conditions for Strongly Starlikeness

We consider strongly starlikeness of order α of functions f(z)= z+an+1zn+1 +··· which are analytic in the unit disc and satisfy the condition of the form ∣∣∣∣f ′(z) ( z f(z) )1+μ −1 ∣∣∣∣< λ, 0< μ < 1, 0< λ< 1.

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

Subordination Criteria for Starlikeness and Convexity

For functions p analytic in the open unit disc U = {z : |z|< 1} with the normalization p(0)= 1, we consider the families [A,−1], −1 0, consisting of p, which have the disc formulation |p−1|< b in U . We then introduce subordination criteria for the choice of p(z)= zf ′(z)/f(z), where f is analytic in U and n...