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Authors: EDUARD ȘTEFAN GRIGORICIUC.
DOI: 10.24193/subbmath. 2021.3.06
Published Online: 2021-09-30
Published Print: 2021-09-30
pp. 479-490
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In this paper, we discuss about normalized holomorphic functions whose derivatives have positive real part. For this class of functions, denoted R, we present a general distortion result (some upper bounds for the modulus of the k-th derivative of a function). We present also some remarks on the functions whose derivatives have positive real part of order $alpha$ (0, 1). More details about these classes of functions can be found in [6], [8], [7, Chapter 4] and [4]. In the last part of this paper, we present two new subclasses of normalized holomorphic functions whose derivatives have positive real part which generalize the classes R and R (alpha)$. For these classes we present some general results and examples.
Mathematics Subject Classification (2010): 30C45, 30C50.
Keywords: univalent function, positive real part, distortion result, coefficient estimates.
