Starlike hypergeometric functions

Starlikeness and convexity results for hypergeometric functions

“…For the other interesting developments for zF (a, b; c; z) in connection with various subclasses of univalent functions, the reader can refer the works of Carlson and Shaffer [5], Merkes and Scott [6], Ruscheweyh and Singh [7] and Cho et al [8].…”

Norm estimates for the Alexander transforms of convex functions of order alpha

“…The following result is implied by the proof of [12,Theorem] (see also [16,Theorem B]). a, b, c be real numbers with 0 a b c. Then the function zF (a, b; c; z) is starlike of order 1 − a/2.…”

On certain subclasses of analytic functions associated with Poisson distribution series

“…Motivated by several earlier results on connections between various subclasses of analytic and univalent functions by using hypergeometric functions (see [9,10,11,12]) and by the recent investigations of Porwal ([6, 8, 7]), in the present paper we determine the necessary and sufficient conditions for F (m, z) to be in our new classes S(k, λ) and C(k, λ) and connections of these subclasses with R τ (A, B). Finally, we give conditions for the integral…”