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Abstract
We continue to investigate the relation of close-to-convex harmonic mappings versus their analytic counterpart. Our starting point is the investigation initiated by Clunie and Sheil-Small [J. Clunie and T. Sheil-Small, Harmonic univalent mappings, Ann. Acad. Sci. Fenn. Ser. A.I. Math. 9 (1984), pp. 3–25] and further developments by Chuaqui and Hernandez [M. Chuaqui and R. Hernandez, Univalent harmonic mappings and linearly connected domains, J. Math. Anal. Appl. 332 (2007), pp. 1189–1194], and Bshouty and Lyzzaik [D. Bshouty and A. Lyzzaik, Close-to-convexity criteria for planar harmonic mappings, Complex Anal. Oper.Theory (to appear)].
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Acknowledgements
The work of the first two authors is supported by the European Science Foundation Networking Program HCAA. The second author is supported also by the project (SR/FTP/MS-17/2007) sanctioned by the DST, New Delhi. This work was initiated during the visit of the second and third authors to the Technion, Israel, and they thank the Technion for its financial support and kind hospitality.