Advanced search
Publication Cover
Complex Variables and Elliptic Equations
An International Journal
Volume 53, 2008 - Issue 9
Submit an article Journal homepage
108
Views
24
CrossRef citations to date
0
Altmetric
Original Articles

Landau's theorems for biharmonic mappings

Ming-Sheng Liu School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, PR ChinaCorrespondence[email protected]
Pages 843-855 | Received 20 Jan 2008, Accepted 18 Apr 2008, Published online: 22 Sep 2010

Citations (24)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (4)

Xi Luo & Ming-Sheng Liu. (2020) Landau–Bloch type theorems for certain biharmonic mappings. Complex Variables and Elliptic Equations 65:11, pages 1938-1949.
Read now
Ming-Sheng Liu & Zhen-Xing Liu. (2014) Landau-type theorems for p-harmonic mappings or log-p-harmonic mappings. Applicable Analysis 93:11, pages 2462-2477.
Read now
Yu-Can Zhu & Ming-Sheng Liu. (2013) Landau-type theorems for certain planar harmonic mappings or biharmonic mappings. Complex Variables and Elliptic Equations 58:12, pages 1667-1676.
Read now
Suheil Khuri. (2013) On the Properties of a Class of Polyharmonic Functions. Mathematical Modelling and Analysis 18:2, pages 219-235.
Read now

Articles from other publishers (20)

Jieling Chen & Mingsheng Liu. (2023) Estimate on the Bloch constant for certain harmonic mappings under a differential operator. Acta Mathematica Scientia 44:1, pages 295-310.
Crossref
Ming-Sheng Liu & Saminathan Ponnusamy. (2023) Landau-type theorems for certain bounded bi-analytic functions and biharmonic mappings. Canadian Mathematical Bulletin, pages 1-14.
Crossref
Xi Luo, Ming-Sheng Liu & Ting Li. (2023) Landau-Bloch type theorems of certain subclasses of biharmonic mappings. Filomat 37:2, pages 403-416.
Crossref
Xi Luo & Ming-Sheng Liu. (2022) Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings. Computational Methods and Function Theory.
Crossref
Adel Khalfallah, Fathi Haggui & Mohamed Mhamdi. (2021) Generalized harmonic functions and Schwarz lemma for biharmonic mappings. Monatshefte für Mathematik 196:4, pages 823-849.
Crossref
Qinghong Luo & Saminathan Ponnusamy. (2020) One Parameter Family of Univalent Polyharmonic Mappings. Bulletin of the Malaysian Mathematical Sciences Society 44:2, pages 839-856.
Crossref
Mingsheng Liu & Lifang Luo. (2020) Precise values of the Bloch constants of certain log-p-harmonic mappings. Acta Mathematica Scientia 41:1, pages 297-310.
Crossref
Shi-Fei Chen & Ming-Sheng Liu. (2020) Landau-type theorems and bi-Lipschitz theorems for bounded biharmonic mappings. Monatshefte für Mathematik 193:4, pages 783-806.
Crossref
Qinghua Jiang, Fanning Meng & Guoqiang Dang. (2020) Normality of the p-Harmonic and Log-p-Harmonic Mappings. Journal of Function Spaces 2020, pages 1-7.
Crossref
Ming-Sheng Liu & Li-Fang Luo. (2019) Landau-Type Theorems for Certain Bounded Biharmonic Mappings. Results in Mathematics 74:4.
Crossref
Xiao-Xia Bai & Ming-Sheng Liu. (2018) Landau-Type Theorems of Polyharmonic Mappings and log-p-Harmonic Mappings. Complex Analysis and Operator Theory 13:2, pages 321-340.
Crossref
Mingsheng Liu, Lin Xie & Li-Mei Yang. (2017) Landau's theorems for biharmonic mappings (II). Mathematical Methods in the Applied Sciences 40:7, pages 2582-2595.
Crossref
Peijin Li, S.A. Khuri & Xiantao Wang. (2016) On certain geometric properties of polyharmonic mappings. Journal of Mathematical Analysis and Applications 434:2, pages 1462-1473.
Crossref
Ming-Sheng Liu, Zhen-Xing Liu & Jun-Feng Xu. (2014) Landau-Type Theorems for Certain Biharmonic Mappings. Abstract and Applied Analysis 2014, pages 1-7.
Crossref
J. Chen, A. Rasila & X. Wang. (2014) Landau’s theorem for polyharmonic mappings. Journal of Mathematical Analysis and Applications 409:2, pages 934-945.
Crossref
Zhi-Gang Wang, Zhi-Hong Liu & Ying-Chun Li. (2013) On the linear combinations of harmonic univalent mappings. Journal of Mathematical Analysis and Applications 400:2, pages 452-459.
Crossref
Yusuf Abu Muhanna & Rosihan M. Ali. (2013) Biharmonic Maps and Laguerre Minimal Surfaces. Abstract and Applied Analysis 2013, pages 1-9.
Crossref
Peijin Li & Xiantao Wang. (2011) Landau?s theorem for log-p-harmonic mappings. Applied Mathematics and Computation.
Crossref
S. H. Chen, S. Ponnusamy & X. Wang. (2010) Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings. Complex Analysis and Operator Theory 5:3, pages 901-916.
Crossref
Sh. Chen, S. Ponnusamy & X. Wang. (2011) Bloch constant and Landau's theorem for planar p-harmonic mappings. Journal of Mathematical Analysis and Applications 373:1, pages 102-110.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.