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The class of functions defined by differential integral operators

100%

Trojnar-Spelina L.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1999

tom z. 23 [175]

145-160

In this paper we consider the class of functions with negative coefficients denned by differential integral operators. Among others the necessary and sufficient condition for a function f to be in the studied class is presented.

Second order differential subordinations and certain subordination relations

86%

Kowalczyk J.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

tom z. 26 [199]

97-106

In the present paper the second order differential subordination (1 - alpha)f(z/z + alphaf'{z) + betazf(z) [...] 1 + Mz \z is an element of U) is investigated. The best dominant of subordination (1) is founded. Connections between subordination (1) and subordination of f(z)/z, f'{z) are given. Further the convexity of the function / satisfying the subordination (1) for special choice of parameters a, alpha, beta and M are derived.

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

86%

Singh S. , Gupta S.

Demonstratio Mathematica

2005

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 differential subordination for circular domains

86%

Lecko A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

tom z. 22 [170]

101-108

Let U = {z : \z\ < 1} denote the unit disk. For A and B such that -1

On certain subclasses of close-to-convex and

72%

Wang Z.-G. , Jiang Y.-P.

Journal of Mathematics and Applications

2007

tom Vol. 29

167-179

In the present paper, the authors introduce two new subclasses S(sup k) (sub sc) (γ, α β) of close-to-convex functions and C(sup k) (sub sc) (γ, α β) of quasi-convex functions with respect to 2k-symmetric conjugate points. The inclusion and subordination relationships, convolution conditions for these classes are provided. The coefficient inequalities, integral representations and sufficient conditions for functions belonging to these classes are also provided.

Differential subordinationfor domains bounded by hyperbolas

58%

Kanas S. , Lecko A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1999

tom z. 23 [175]

61-70

Let the function pa,b,s-so with a, b real, nonnegative numbers and s, so is an element of R, be a conform al mapping of the unit disk onto a hyperbolic domain. We establish the conditions udner which the differential subordination of the type p(z) +[...]zp'(z) -< pa,b,s-so(^) yields p -< pa,b,s- so(z) yields p [...] pa,b,s in U. Some applications of obtained results are given.

On certain subclasses of p-valently analytic functions of order alpha

58%

Aouf M.

Demonstratio Mathematica

2007

tom Vol. 40, nr 2

317-330

The object of the present paper is to derive various properties and char- acteristics of certain subclasses of p-valently analytic functions of order alpha in the open unit disc by using the techniques involving the Briot-Bouquet differential subordination.