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. Ourâ€¦ (More)

Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, asâ€¦ (More)

We consider the class of univalent functions defined by the conditions f(z)/z â‰ 0 and |(z/f(z))â€²â€²| â‰¤Î±,|z|< 1, where f(z)= z+Â·Â·Â· is analytic in |z|< 1 and 0<Î±â‰¤ 2.

for some Î± (0 Î±< 1). We denote by p(Î±) the subclass of p consisting of functions which are p-valently convex of order Î± in U. In particular, we denote 1(0)= . A function f(z)âˆˆ 1 is said to beâ€¦ (More)

The Carlson-Shaffer operator L(a, c)f = Ï†(a, c) âˆ— f, where f(z) = z+ a2z + Â· Â· Â· is analytic in the unit disk E = {z : |z| < 1} and Ï†(a, c; z) is an incomplete beta function, is used to define theâ€¦ (More)