Some remarks on certain Bazilevic functions

ON CERTAIN SUBCLASS OF p-VALENTLY BAZILEVIC FUNCTIONS

We introduce a subclass Mp(λ, μ,A,B) of p-valent analytic functions and derive certain properties of functions belonging to this class by using the techniques of Briot-Bouquet differential subordination. Further, the integral preserving properties of Bazilevic functions in a sector are also considered.

Some Remarks on Approximation of Plurisubharmonic Functions

Let Ω be a domain in Cn. An upper semicontinuous function u : Ω → [−∞,∞) is said to be plurisubharmonic if the restriction of u to each complex line is subharmonic (we allow the function identically −∞ to be plurisubharmonic). We say that u is strictly plurisubharmonic if for every z0 ∈ Ω there is a neigbourhood U of z0 and λ > 0 such that u(z) − λ|z|2 is plurisubharmonic on U . We write PSH(Ω)...

Some Remarks on Monge-ampère Functions

The space of Monge-Ampère functions is a rather large function space with the property that, if u is a Monge-Ampère function, then the determinant of the Hessian can be identified with a well-defined Radon measure, denoted DetDu. Moreover, the map u 7→ DetDu is continuous in a natural weak topology on the space of Monge-Ampère functions. These properties make Monge-Ampère functions potentially ...

On strongly Bazilevic functions associated with generalized Robertson functions

Some Remarks on the Measurability of Certain Sets

The present note contains some elementary remarks on sets defined by simple geometric properties. Our main tool will be the Lebesgue density theorem. First we introduce a few notations : d(a, b) denotes the distance from a to b and Six, r) the open sphere of center x and radius r. A point x of a set A is said to be of metric density 1 if to every e there exists a ô such that AC\S{x, r) , r < 5,...