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7 Demonstratio Mathematica

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Integral operator which preserves the univalence in the upper half-plane

100%

Blezu D. , Pascu N. N. , Pascu R. N.

tom Vol. 36, nr 1

77--81

In this paper, using the Pfaltzgraff integral operator and the so called "parametric circles method" introduced by N. N.Pascu (1999), we can obtain an univalence criterion for the analytic function denned in the upper half-plane and also for comparison two univalence criteria obtained by a simple composition of functions.

Generalizations of Hadamard products of certain meromorphic univalent functions with positive coefficients

75%

Aouf M. , Silverman H.

tom Vol. 41, nr 2

381-388

The authors establish certain results concerning the generalized Hadamard products of certain meromorphic univalent functions with positive coefficients analagous to the results due to Choi et al. (J. Math. Anal. Appl. 199(1996), 495-501).

Linear invariance and integral operators of univalence functions

75%

Dorff M. , Szynal J.

tom Vol. 38, nr 1

47--57

In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains (1), where / belongs to the linear invariant family, and thereby we obtain information about the univalence of (1). In particular, we determine the order of this minimal invariant family in the cases of univalent and convex univalent functions in D. As a result, we find the radius of close-to-convexity and the lower bound for the radius of univalence for the minimal invariant family in the case of convex univalent functions. This allows us to determine the exact region for (a, (3) where the corresponding minimal invariant family is univalent and close-to-convex. These results are sharp and generalize those which were obtained in [11].

Univalence criterion for certain integral operators

75%

Hamada H.

tom Vol. 38, nr 1

43--46

Pescar investigated the univalence of certain integral operators. We will show that the results are obtained by the Schwarz lemma. We will also give some generalizations.

On a problem H. S. Al-Amiri and M. O. Reade

75%

Singh S. , Gupta S.

tom Vol. 38, nr 2

303--311

In the present paper, the authors investigate the univalence of the functions f, analytic in -E, f(O) = 0, f'(0) = 1 and which satisfy Re [(1 - alfa)f'(z) + alfa (1+ zf''(z): f'(z)] >beta, z is an element of E, where alfa > 0 and 0 < beta < 1. The univalence of such functions has already been established in the case when alfa < 0 and beta = 0 by H. S. Al-Amiri and M. 0. Reade in 1975.

On certain subclass of analytic functions with complex order

63%

Aouf M. K. , Al-amri B. A.

tom Vol. 36, nr 4

827--838

On the coefficients of a class of univalent functions

51%

Şerb I.

tom Vol. 38, nr 3

567--578

We consider a class of univalent functions which verify a strong Milin type condition for logarithmic coefficients. This class contains all alfa-Koebe spirallike functions, all extremal points of the class of typically real functions, together with their rotations and multiplicative "compositions". We find some extremal functions of this class.