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Complex Variables and Elliptic Equations
An International Journal
Volume 58, 2013 - Issue 12
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Articles

Solution to an open problem on convolutions of harmonic mappings

Liulan Li Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, Hunan 421008, People's Republic of China
&
Saminathan Ponnusamy Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IndiaCorrespondence[email protected]
Pages 1647-1653 | Received 01 Mar 2012, Accepted 08 Jun 2012, Published online: 25 Sep 2012

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Michael Dorff, Samaneh G. Hamidi, Jay M. Jahangiri & Elif Yaar. (2021) Convolutions of planar harmonic strip mappings. Complex Variables and Elliptic Equations 66:11, pages 1904-1921.
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Bo-Yong Long & Hua-Ying Huang. (2020) On directional convexity of harmonic mappings in the plane. Quaestiones Mathematicae 43:10, pages 1435-1447.
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Articles from other publishers (24)

Raj Kumar & Sarika Verma. (2021) On Construction and Convolution Properties of Univalent Harmonic Mappings. Bulletin of the Iranian Mathematical Society 48:4, pages 1539-1552.
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Ankur Raj, Sumit Nagpal & V. Ravichandran. (2021) On the Product of Planar Harmonic Mappings. Computational Methods and Function Theory 21:3, pages 427-452.
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Ahmad Sulaiman Ahmad El-Faqeer, Zhen Chuan Ng & Shamani Supramaniam. (2021) On Convolution and Convex Combination of Harmonic Mappings. Journal of Mathematics 2021, pages 1-12.
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S. Yalçın, A. Ebadian & S. Azizi. (2021) A Proof of a Conjecture on the Convolution of Harmonic Mappings and Some Related Problems. Ukrainian Mathematical Journal 73:2, pages 329-336.
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S. Yalçın, A. Ebadian & S. Azizi. (2021) A proof of a conjecture on convolution of harmonic mappings and some related problems. Ukrains’kyi Matematychnyi Zhurnal 73:2, pages 283-288.
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Md Firoz Ali, Vasudevarao Allu & Nirupam Ghosh. (2020) A convolution property of univalent harmonic right half-plane mappings. Monatshefte für Mathematik 193:4, pages 729-736.
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Subzar Beig. (2020) On Convolution of Harmonic Mappings. Complex Analysis and Operator Theory 14:4.
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Stacey Muir. (2019) Convolutions of Normalized Harmonic Mappings. Computational Methods and Function Theory 19:4, pages 583-599.
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LIULAN LI & SAMINATHAN PONNUSAMY. (2019) NOTE ON THE CONVOLUTION OF HARMONIC MAPPINGS. Bulletin of the Australian Mathematical Society 99:03, pages 421-431.
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Zhi-Hong Liu, Zhi-Gang Wang, Antti Rasila & Yue-Ping Jiang. (2019) Convolutions of Harmonic Right Half-Plane Mappings with Harmonic Strip Mappings. Bulletin of the Malaysian Mathematical Sciences Society 42:3, pages 1199-1212.
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ZhiHong Liu & Saminathan Ponnusamy. (2016) Univalency of Convolutions of Univalent Harmonic Right Half-Plane Mappings. Computational Methods and Function Theory 17:2, pages 289-302.
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Stacey Muir. (2016) Convex Combinations of Planar Harmonic Mappings Realized Through Convolutions with Half-Strip Mappings. Bulletin of the Malaysian Mathematical Sciences Society 40:2, pages 857-880.
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Saminathan Ponnusamy & Jinjing Qiao. (2017) Characterization of univalent harmonic mappings with integer or half-integer coefficients. Analysis 37:1, pages 23-38.
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Liulan Li & Saminathan Ponnusamy. (2016) Injectivity of sections of convex harmonic mappings and convolution theorems. Czechoslovak Mathematical Journal 66:2, pages 331-350.
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Raj Kumar, Sushma Gupta, Sukhjit Singh & Michael Dorff. (2016) An application of Cohn's rule to convolutions of univalent harmonic mappings. Rocky Mountain Journal of Mathematics 46:2.
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YingChun Li & ZhiHong Liu. (2016) Convolutions of harmonic right half-plane mappings. Open Mathematics 14:1, pages 789-800.
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Zhi-Gang Wang, Zhi-Hong Liu & Ying-Chun Li. (2016) ON CONVOLUTIONS OF HARMONIC UNIVALENT MAPPINGS CONVEX IN THE DIRECTION OF THE REAL AXIS. Journal of Applied Analysis & Computation 6:1, pages 145-155.
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Raj Kumar, Michael Dorff, Sushma Gupta & Sukhjit Singh. (2015) Convolution Properties of Some Harmonic Mappings in the Right Half-Plane. Bulletin of the Malaysian Mathematical Sciences Society 39:1, pages 439-455.
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YUE-PING JIANG, ANTTI RASILA & YONG SUN. (2015) A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS. Bulletin of the Korean Mathematical Society 52:6, pages 1925-1935.
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Liulan Li & Saminathan Ponnusamy. (2015) Sections of stable harmonic convex functions. Nonlinear Analysis: Theory, Methods & Applications 123-124, pages 178-190.
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Liulan Li & Saminathan Ponnusamy. (2014) Convolutions of Harmonic Mappings Convex in One Direction. Complex Analysis and Operator Theory 9:1, pages 183-199.
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S. Ponnusamy & A. Sairam Kaliraj. (2014) Univalent harmonic mappings convex in one direction. Analysis and Mathematical Physics 4:3, pages 221-236.
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Zach Boyd & Michael Dorff. 2014. Current Topics in Pure and Computational Complex Analysis. Current Topics in Pure and Computational Complex Analysis 21 46 .
Zhi-Hong Liu & Ying-Chun Li. (2013) The Properties of a New Subclass of Harmonic Univalent Mappings. Abstract and Applied Analysis 2013, pages 1-7.
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