More precisely, unless stated otherwise, in all later discussions, let Ω be a fixed, nonempty, closed and bounded domain in R m and let p : Ω → ( 0, ∞ ) be a fixed function which satisfies ∫ Ω p d ω = 1.
Let,,,, is a fixed function from, for example,.
Assume that is a fixed integer and is a fixed function in.
where is a fixed function and is a suitably normalized function with positive real part.
The mapping is defined in the following way:, where is a fixed function, for example,.
Let,,,, and defined by, where is a fixed function, for example,.
As before, it is assumed that is a fixed integer, is a fixed function in, and is a convex univalent function with positive real part in satisfying.
It is assumed in the sequel that is a fixed integer, is a fixed function in, and is a convex univalent function with positive real part in satisfying.
where is a fixed function in and is a suitably normalized analytic function with positive real part.
Let be a fixed function in, and let be a convex univalent function with positive real part in and.
