Geodesic
Rotations and convolutions of harmonic convex mappings
Filomat, Tome 36 (2022) no. 11, p. 3845

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DOI

In this paper, we mainly consider the convolutions of slanted half-plane mappings and strip mappings of the unit disk D. If f 1 is a slanted half-plane mapping and f 2 is a slanted half-plane mapping or a strip mapping, then we prove that f 1 * f 2 is convex in some direction if f 1 * f 2 is locally univalent in D. We also obtain two sufficient conditions for f 1 * f 2 to be locally univalent in D. Our results extend many of the recent results in this direction. Moreover, we consider a class of harmonic mappings including slanted half-plane mappings and strip mappings, and as a consequence, we prove that the any convex combination of such locally univalent and sense-preserving mappings is also convex.
DOI : 10.2298/FIL2211845L
Classification : 31A05, 30C45, 30C20
Keywords: Harmonic, univalent, slanted half-plane mappings, convex mappings, convex in a direction, and convolution 
Liulan Li; Saminathan Ponnusamy. Rotations and convolutions of harmonic convex mappings. Filomat, Tome 36 (2022) no. 11, p. 3845 . doi: 10.2298/FIL2211845L
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     author = {Liulan Li and Saminathan Ponnusamy},
     title = {Rotations and convolutions of harmonic convex mappings},
     journal = {Filomat},
     pages = {3845 },
     year = {2022},
     volume = {36},
     number = {11},
     doi = {10.2298/FIL2211845L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2211845L/}
}
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