Univalence criteria and quasiconformal extension of a general integral operator

E. Deniz; S. Kanas; H. Orhan

doi:10.37863/umzh.v74i1.1148

E. Deniz Kafkas Univ., Kars, Turkey https://orcid.org/0000-0002-9570-8583
S. Kanas Univ. Rzeszów, Poland
H. Orhan Atatürk Univ., Erzurum, Turkey

DOI: https://doi.org/10.37863/umzh.v74i1.1148

Keywords: Univalent function; Quasiconformal mapping; Univalence condition; Integral operator; Loewner chain.

Abstract

UDC 517.5

We give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker’s method. Further, new univalence criteria and the significant relationships with other results are given. A number of known univalence conditions would follow upon specializing the parameters involved in main results.

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