Radius of close-to-convexity and fully starlikeness of harmonic mappings

References

• Clunie JG, Sheil-Small T. Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A.I. 1984;9:3–25.
   Google Scholar
• Duren , P . 2004 . Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics, 156 , Cambridge : Cambridge Univ. Press .
   Google Scholar
• Lewy , H . 1936 . On the nonvanishing of the Jacobian in certain one-to-one mappings . Bull. Amer. Math. Soc. , 42 : 689 – 692 .
   Google Scholar
• Xiao-Tian , Wang and Xiang-Qian , Liang . 2001 . Precise coefficient estimates for close-to-convex harmonic univalent mappings . J. Math. Anal. Appl. , 263 : 501 – 509 .
   Web of Science ®Google Scholar
• Chuaqui , M , Duren , P and Osgood , B . 2004 . Curvature properties of planar harmonic mappings . Comput. Methods Funct. Theory. , 4 : 127 – 142 .
   Google Scholar
• Bshouty , D and Lyzzaik , A . 2010 . Problems and conjectures in planar harmonic mappings: in the Proceedings of the ICM2010 Satellite Conference: International Workshop on Harmonic and Quasiconformal Mappings (HQM2010). In: Minda D, Ponnusamy S, Shanmugalingam N, editors. Special issue in: J . Analysis. , 18 : 69 – 82 .
   Google Scholar
• Ruscheweyh S, Salinas L. On the preservation of direction-convexity and the Goodman-Saff conjecture. Ann. Acad. Sci. Fenn. Ser. A I Math. 1989;14:63–73.
   Google Scholar
• Sheil-Small , T . 1990 . Constants for planar harmonic mappings . J. London Math. Soc. , 42 : 237 – 248 .
   Web of Science ®Google Scholar
• Chen , H , Gauthier , PM and Hengartner , W . 2000 . Bloch constants for planar harmonic mappings . Proc. Amer. Math. Soc. , 128 : 3231 – 3240 .
   Web of Science ®Google Scholar
• Dorff , M and Nowak , M . 2004 . Landau’s theorem for planar harmonic mappings . Comput. Methods Funct. Theory. , 4 : 151 – 158 .
   Google Scholar
• Grigoryan , A . 2006 . Landau’s theorem for planar harmonic mappings . Complex Var. Elliptic Equ. , 51 : 81 – 87 .
   Google Scholar
• Liu MSh. Landau’s theorem for biharmonic mappings. Complex Var. Elliptic Equ. 2008;9: 843-855.
   Google Scholar
• Liu , MSh . 2009 . Estimates on Bloch constants for planar harmonic mappings . Sci. China Ser. A-Math. , 52 ( 1 ) : 87 – 93 .
   Google Scholar
• Chen , Sh , Ponnusamy , S and Wang , X . 2011 . Coefficient estimates and Landau-Bloch’s constant for planar harmonic mappings . Bull. Malaysian Math. Sciences Soc. , 34 : 255 – 265 .
   Web of Science ®Google Scholar
• Bharanedhar SV, Ponnusamy S. Coefficient conditions for harmonic univalent mappings and hypergeometric mappings. Rocky Mountain J. Math. in press. Available from: http://arxiv.org/pdf/1109.0925v2.pdf
   Google Scholar
• Ponnusamy S, Yamamoto H, Yanagihara H. Variability regions for certain families of harmonic univalent mappings. Complex Var. Elliptic Equ. 2013;58:23–34. Available from http://dx.doi.org/10.1080/17476933.2010.551200
   Google Scholar
• Silverman H. Univalent functions with negative coefficients. J. Math. Anal. Appl. 1998;220: 283-289.
   Google Scholar
• Chen , Sh , Ponnusamy , S and Wang , X . 2011 . Bloch and Landau’s theorems for planar -harmonic mappings . J. Math. Anal. and Appl. , 373 : 102 – 110 .
   Web of Science ®Google Scholar