MATHEMATICAL MODEL FOR THE RESPONSE OF HPA AXIS APPLYING GOMPERTZ - MAKEHAM DISTRIBUTION IN ASSOCIATION WITH ANALYTIC UNIVALENT FUNCTIONS

The study here is to find the activity of Hypothalamic Pituitary Adrenal axis - HPA which is a major part of human system which controls reaction to stress by finding Cortisol level and the objective is to observe the response of the system over time due to stress by applying the Gompertz - Makeham distribution. Here we develop two functions f 1(z)and f 2(z) by using the class of analytic univalent functions in the open unit disc whose coefficients are considered as Probability density function of the above mentioned distribution, for which the Subordination property, Convex and Star likeness hold. Current study leads us to a real life application by considering the effects on the response of HPA axis to acute stress. The concluded results coincide with the medical findings.

SUBCLASSES OF MULTIVALENT NON-BAZILEVIC FUNCTIONS DEFINED WITH HIGHER ORDER DERIVATIVES

By making use of the principle of subordination, we introduce a certain class of multivalent non-Bazilevic functions with higher order. Also, we obtain subordination property, inclusion result, and inequality properties of this class. The results presented here would provide extensions of those given in earlier works.

A New Class of Meromorphic Functions Associated with Spirallike Functions

We introduce a new class of meromorphic functions associated with spirallike functions. Such results as subordination property, integral representation, convolution property, and coefficient inequalities are proved.

HILBERT SPACE OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE MODIFIED BESSEL FUNCTION AND RELATED ORTHOGONAL POLYNOMIALS

Let μ be a probability measure on I ⊂ ℝ with finite moment of all orders and γα, c1, 2 be a probability measure on ℂ which is expressed by the modified Bessel function. In this paper, we shall first consider operators B-, B+, B° and express them in terms of bosonic creation and annihilation operators. Secondly, we shall construct the Hilbert space of analytic L2 functions with respect to γα, c1, 2, [Formula: see text]. It will be seen that the Sμ-transform under certain conditions is a unitary operator from L2 (I, μ) onto [Formula: see text]. Moreover, we shall give explicit examples including Laguerre, Meixner and Meixner–Pollaczek polynomials and explain how the Hilbert space [Formula: see text] and B-, B+, B° are related from the probabilistic point of view. It will also be given the relationship between the heat kernel on ℂ and γα, c1, 2 (subordination property).