Current Topics in Analytic Function Theory

The Relationships Between p−valent Functions and Univalent Functions

“…Remark 1: (7) p−valent integral operator, for p = 1, was studied by Seenivasagan and Breaz (see [14]) (see also the recent investigations on this subject by Baricz and Frasin [2] and Srivastava, Deniz and Orhan [15]). We note that if α i = α for all i = 1, n and p = 1, then the p−valent integral operator F p α1,...,αn,β (z) reduces to the operator F 1 α,β (z) which is related closely to some known integral operators investigated earlier in Geometric Functions Theory (see, for details, [16]). The operators F 1 α,β (z) and F 1 α,α (z) were studied by Breaz and Breaz (see [4]) and Pescar (see [12]), respectively.…”

The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

“…The operator L(a, c) is analytic in U and plays an important role in Geometric Functions Theory; see for example [24], [14], [21] and [9].…”

Certain results on subordinations associated with a differintegral operator

“…Also, by choosing the function ϕ suitably in (3) and (4), we obtain several other function classes which have been investigated in recent past ( [14], [15]). If we restrict our attention to the functions ϕ which map U onto a disc or a half-plane, then we obtain the classes…”