for unbounded G, where f is an

analytic function on G with known boundary values on [GAMMA].

For two

analytic functions f, g [member of] S we say that f is subordinate to g denoted by f [?

This class is called convex class of

analytic function.

In [7], the following Carleman boundary value problem for

analytic functions is given: Problem [C.

H](n) we may express the

analytic functions h and g as

Srivastava, The Hardy space of

analytic functions associated with certain one-parameter families of integral operators, J.

Theorem 1 Let f be an

analytic function on the circle [K.

1 provides sufficient conditions to ensure that all the roots of a polynomial Q (y) are contained in the range of an

analytic function y (z) when there exists another polynomial P(z), of the same degree as Q (y), such that P(z) = Q (y(z)) in a neighborhood of z = 0.

Throughout this paper, we assume that [phi] is an

analytic function in D of the form

3, there exists an

analytic function p [member of] P in the unit disc E with p(O) = 1 and [Real part]{p(z)}>0 such that

In the present investigation, we obtain sufficient conditions for a function containing Noor Integral operator of normalized

analytic function f, by applying a method based on the differential subordination,

We thus have the task of finding a closed-form, two-dimensional

analytic function [Y.