1. Properties of Logharmonic Mappings.
- Author
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Meng, Liqing, Ponnusamy, Saminathan, and Qiao, Jinjing
- Abstract
The main aim of this paper is to investigate properties of certain class of logharmonic mappings. Initially, we establish the argument principle of sense-preserving mappings F = h g ¯ + H G ¯ , where h, g, H and G are analytic functions. As applications, we obtain a direct extension of Rouché’s theorem, open mapping theorem and minimal area image of sense-preserving logharmonic mappings. Furthermore, we present an estimate for the modulus of the partial derivative of K-quasiconformal logharmonic mappings, and by using it, we get a Schwarz type lemma of K-quasiconformal logharmonic mappings. Finally, we obtain estimates of h ′ ′ (0) 2 and g ′ ′ (0) 2 for univalent sense-preserving logharmonic mappings f = h g ¯ in the unit disk. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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