On problems of univalence for the class $TR(1/2)$

M. Sobczak-Kneć, P. Zaprawa

Lublin University of Technology, Department of Applied Mathematics, Lublin

Abstract: In this paper we discuss the class $TR(\frac{1}{2})$ consisted of typically real functions given by the integral formula $f(z) = \int \limits_{-1}^{1}\frac{z}{\sqrt{1-2zt+z^2}}d\mu(t)$, where $\mu$ is the probability measure on $[-1, 1]$.The problems of local univalence, univalence, convexity in the direction of real and imaginary axes are examined. This paper is the continuation of research on $TR(\frac{1}{2})$, especially concerning problems, which results were published in [5].

UDC: 517

Language: English

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