2021
DOI: 10.1155/2021/9188781
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Linear Combinations of Univalent Mappings with Complex Coefficients

Abstract: In this paper, we study the linear combinations of two univalent mappings with complex coefficients, and we derive several sufficient conditions that the linear combinations of these mappings are locally univalent and convex in one direction. Several examples are constructed to demonstrate the main results.

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“…Let 3 ω be the dilatation of 3 f which satisfies the Equation (10). By setting 1 z ω = − , 2 z ω = , and substituting them into Equation (11), we obtain…”
Section: Resultsmentioning
confidence: 99%
“…Let 3 ω be the dilatation of 3 f which satisfies the Equation (10). By setting 1 z ω = − , 2 z ω = , and substituting them into Equation (11), we obtain…”
Section: Resultsmentioning
confidence: 99%