Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 11: Functional theoretic methods, wavelets and applied PDEs on the occasion of Professor Wei Lin’s 80th Birthday and the 30th anniversary of Robert Gilbert visiting China. Guest editors Daoqing Dai, Yuqiu Zhao and Yongzhi Steve Xu
Submit an article Journal homepage
74
Views
2
CrossRef citations to date
0
Altmetric
Articles

Landau-type theorems for p-harmonic mappings or log-p-harmonic mappings

Ming-Sheng LiuSchool of Mathematical Sciences, South China Normal University, Guangzhou510631, Guangdong, People’s Republic of China.Correspondence[email protected]
&
Zhen-Xing LiuSchool of Mathematical Sciences, South China Normal University, Guangzhou510631, Guangdong, People’s Republic of China.
Pages 2462-2477 | Received 24 Nov 2013, Accepted 29 Jan 2014, Published online: 05 Mar 2014

References

  • Chen SH, Ponnusamy S, Wang X. Bloch constant and Landau’s theorem for planar p-harmonic mappings. J. Math. Appl. Appl. 2011;373:102–110.
  • Li P, Ponnusamy S, Wang X. Some properties of planar p-harmonic and log-p-harmonic mappings. Bull. Malays. Math. Sci. Soc. 2013;36:595–609.
  • Abdulhadi Z. On the univalence of functions with logharmonic laplacian. Appl. Math. Comput. 2009;215:1900–1907.
  • Abdulhadi Z, Abu Muhanna Y, Khuri S. On univalent solutions of the biharmonic equation. J. Inequal. Appl. 2005;5:469–478.
  • Abdulhadi Z, Abu Muhanna Y, Khuri S. On some properties of solutions of the biharmonic equation. Appl. Math. Comput. 2006;177:346–351.
  • Abdulhadi Z, Abu Muhanna Y. Landau’s theorem for biharmonic mappings. J. Math. Anal. Appl. 2008;338:705–709.
  • Abdulhadi Z, Abu Muhanna Y, Khuri S. On the univalence of the log-biharmonic mappings. J. Math. Anal. Appl. 2004;289:629–638.
  • Li P, Wang X. Landau’s theorem for log-p-harmonic mappings. Appl. Math. Comput. 2012;218:4806–4812.
  • Mao Zh, Ponnusamy S, Wang X. Schwarzian derivative and Landau’s theorems for log-harmonic mappings. Complex Var. Elliptic Eq. 2013;58:1093–1107.
  • Chen H-H, Gauthier PM, Hengartner W. Bloch constants for planar harmonic mappings. Proc. Amer. Math. Soc. 2000;128:3231–3240.
  • Chen SH, Ponnusamy S, Wang X. Coefficient estimates and Landau-Bloch’s constant for harmonic mappings. Bull. Malays. Math. Sci. Soc. 2011;34:255–265.
  • Dorff M, Nowark M. Landau’s theorem for planar harmonic mappings. Comput. Meth. Funct. Theory. 2004;4:151–158.
  • Grigoryan A. Landau and Bloch theorems for planar harmonic mappings. Comp. Var. Elliptic. 2006;51:81–87.
  • Huang XZ. Estimates on Bloch constants for planar harmonic mappings. J. Math. Anal. Appl. 2008;337:880–887.
  • Landau E. Der Picard-Schottysche Satz und die Blochsche Konstanten. Sitzungsber Press Akad., Wiss. Berlin Phys.-Math Kl; 1926. p. 467–474.
  • Li DZ, Chen XD. Bloch constant of Harmonic mappings. J. Huaqiao Univ. (Nat. Sci.). 2012;33:103–106.
  • Liu MS. Estimates on Bloch constants for planar harmonic mappings. Sci. China Ser. A-Math. 2009;52:87–93.
  • Liu MS. Landau’s theorems for planar harmonic mappings. Comput. Math. Appl. 2009;57:1142–1146.
  • Liu MS. Landau’s theorems for biharmonic mappings. Comp. Var. Elliptic Eq. 2008;53:843–855.
  • Zhu YC, Liu MS. Landau-type theorems for certain planar harmonic mappings or biharmonic mappings. Comp. Var. Ellipt. Eq. 2013;58:1667–1676.
  • Colonna F. The Bloch constant of bounded harmonic mappings. Indiana Univ. Math. J. 1989;38:829–840.
  • Liu MS, Liu ZW, Zhu YC. Landau’s theorems for certainr biharmonic mappings. Acta Math. Sin. 2011;54:69–80. Chinese.
  • Xia XQ, Huang XZ. Estimates on Bloch constants for planar bounded harmonic mappings. Chinese Ann. Math. 2010;31A:769–776. Chinese.

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.