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Certain differential subordinations using a generalized Salagean operator and Ruscheweyh operator

Lupas A. A.

Journal of Mathematics and Applications

2010

Vol. 33

67-72

In the present paper we define a new operator using the generalized Salagean operator and Ruscheweyh operator. Denote by [formula/wzór] the Hadamard product of the generalized Salagean operator [formula/wzór] and Ruscheweyh operator R(n), given by [fomula/wzór] is the class of normalized analytic functions with A1 = A. We study some differential subordinations regarding the operator [formula/wzór].

The study of a class of univalent functions defined by Ruscheweyh differential operator

Taut A. O.

Journal of Mathematics and Applications

2009

Vol. 31

107-115

By using a certain operator D(n), we introduce a class of holomorphic functions Mn(h), h convex function, and we obtain some subordination results. We also show that, for h(z) ≡ α, 0 ≤ α < 1 and z ∈ U, the set Mn(α) is convex and we obtain some new differential subordinations related to certain integral operators.

On a certain subclass of analytic functions defined by Sălăgean and Ruscheweyh operators

Lupas A.

Journal of Mathematics and Applications

2009

Vol. 31

67-76

In the present paper we define a new operator using the Salagean and Ruscheweyh operators. Denote by L(m)(α) the operator given by [wzór], where R(m)f(z) denote the Ruscheweyh derivative, S(m)f(z) is the Salagean operator and [wzór] is the class of normalized analytic functions. A certain subclass, denoted by [wzór], of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class [wzór]. Also, several differential subordinations are established regardind the operator L(m)(α).