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In geometric function theory of a complex variable problems on extremal decomposition with free poles on the unit circle are well known. One of such problem is the problem on maximum of the functional ... where B0, B1, B2,...,Bn, n ≥ 2, are pairwise disjoint domains in C, a0 = 0, |ak| = 1, k = 1, n and γ ∊ (0,n], r(B,a) is the inner radius of the domain B ⊂ C, with respect to a point a ∊ B. In the paper we consider a more general problem in which restrictions on the geometry of the location of points ak, k = 1,n are weakened. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class L(λ, μ, ϕ) of analytic functions f dened in the open unit disk U satisfying the subordination condition that q(z) Dλ+1f(z)/Dλf(z) ≺ ϕ(z) (λ ∈ N0; μ ≥ 0; z ∈ U); where q(z) = (z/Dλf(z))μ-2, Dλ is the Sλalλagean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coeficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f(z), sharp bounds for the initial coeficient and for the Fekete-Szego functional are determined, and also some integral representations are given. [ABSTRACT FROM AUTHOR]

Let k - ST[A, B], k ≥ 0, -1 ≤ B < A ≤ 1 be the class of normalized analytic functions defined in the open unit disk satisfying R((B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)) > k/(B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)-1/ and let k - UCV [A,B], k ≥ 0, -1 ≤ B < A ≤ 1 be the corresponding class satisfying R((B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)) > k/(B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)-1/. For an appropriate δ > 0, the δ neighborhood of a function f ∊ k -UCV[A, B] is shown to consist of functions in the class k - ST[A, B]. [ABSTRACT FROM AUTHOR]

In this paper, the flow of an incompressible non Newtonian fluid between two eccentric cylinders is considered. The aim of this study is to determine the flow in the case of the stationary movement of some viscous fluids between two eccentric cylinders with the generators parallel with Oz axis. Using the Mobius conformal mapping are obtained two concentric cylinders. The expression of velocity is deduced with the separation of variable method. [ABSTRACT FROM AUTHOR]

In this paper we obtain an univalence criterion for analytic functions in the unit disk. [ABSTRACT FROM AUTHOR]