2017
Том 69
№ 9

All Issues

Orhan H.

Articles: 2
Brief Communications (English)

Univalence criteria and quasiconformal extensions

Çaǧlar M., Orhan H.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1147-1151

We establish more general conditions for the univalence of analytic functions in the open unit disk $U$. In addition, we obtain a refinement to the criterion of quasiconformal extension for the main result.

Article (English)

Classes of Analytic Functions Defined by a Differential Operator Related to Conic Domains

Deniz E., Orhan H., Sokół J.

↓ Abstract

Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1217–1231

Let $A$ be the class of functions $f(z) = z + ∑_{k = 2}^{ ∞} a_k z^k$ analytic in an open unit disc $∆$. We use a generalized linear operator closely related to the multiplier transformation to study certain subclasses of $A$ mapping $∆$ onto conic domains. Using the principle of the differential subordination and the techniques of convolution, we investigate several properties of these classes, including some inclusion relations and convolution and coefficient bounds. In particular, we get many known and new results as special cases.