Coefficient estimates and radii problems for certain classes of polyharmonic mappings

References

• Duren P. Harmonic mappings in the plane. Cambridge: Cambridge University Press; 2004.
   Google Scholar
• Chen Sh, Ponnusamy S, Wang X. Bloch and Landau’s theorems for planar p-harmonic mappings. J. Math. Anal. Appl. 2011;373:102–110.
   Web of Science ®Google Scholar
• Chen Sh, Ponnusamy S, Wang X. Landau’s theorem for p-harmonic mappings in several complex variables. Ann. Polon. Math. 2012;103:67–87.
   Web of Science ®Google Scholar
• Aronszajn N, Creese T, Lipkin L. Polyharmonic functions. Notes taken by Eberhard Gerlach. Oxford Mathematical Monographs. New York (NY): Oxford Science Publications. The Clarendon Press, Oxford University Press; 1983.
   Google Scholar
• Abdulhadi Z, Abu Muhanna Y. Landau’s theorem for biharmonic mappings. J. Math. Anal. Appl. 2008;338:705–709.
   Web of Science ®Google Scholar
• Abdulhadi Z, Abu Muhanna Y, Khuri S. On univalent solutions of the biharmonic equation. J. Inequal. Appl. 2005;5:469–478.
   Google Scholar
• Abdulhadi Z, Abu Muhanna Y, Khuri S. On some properties of solutions of the biharmonic equation. Appl. Math. Comput. 2006;177:346–351.
   Web of Science ®Google Scholar
• Chen J, Wang X. On certain classes of biharmonic mappings defined by convolution. Abstr. Appl. Anal. 2012, Article ID 379130, 10pp. doi:10.1155/2012/379130.
   Web of Science ®Google Scholar
• Happel J, Brenner H. Low Reynolds number hydrodynamics with special applications to particulate media. Englewood Cliffs (NJ): Prentice-Hall; 1965.
   Google Scholar
• Khuri SA. Biorthogonal series solution of Stokes flow problems in sectorial regions. SIAM J. Appl. Math. 1996;56:19–39.
   Web of Science ®Google Scholar
• Langlois WE. Slow viscous flow. New York (NY): Macmillan; 1964.
   Google Scholar
• Chen J, Rasila A, Wang X. On polyharmonic univalent mappings. Math. Rep. 2013;15:343–357.
   Google Scholar
• Chen J, Rasila A, Wang X. Starlikeness and convexity of polyharmonic mappings. Bull. Belg. Math. Soc. Simon Stevin. 2014;21:67–82.
   Web of Science ®Google Scholar
• Chen J, Rasila A, Wang X. Landau’s theorem for polyharmonic mappings. J. Math. Anal. Appl. 2014;409:934–945.
   Web of Science ®Google Scholar
• Clunie JG, Sheil-Small T. Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A. I. 1984;9:3–25.
   Google Scholar
• Fekete M, Szegő G. Eine bemerkung über ungerade schlichte functionen. J. London Math. Soc. 1933;8:85–89.
   Google Scholar
• Abdel HR, Gawad D, Thomas K. The Fekete–Szegő problem for strong close-to-convex functions. Proc. Amer. Math. Soc. 1992;114:345–349.
   Web of Science ®Google Scholar
• Koepf W. On the Fekete–Szegő problem for close-to-convex functions. Proc. Amer. Math. Soc. 1987;101:89–95.
   Web of Science ®Google Scholar
• Keogh FR, Merkes EP. A coefficient inequality for certain classes of analytic functions. Proc. Amer. Math. Soc. 1969;20:8–12.
   Web of Science ®Google Scholar
• Koepf W. On the Fekete–Szegő problem for close-to-convex functions II. Arch. Math. 1987;49:420–433.
   Web of Science ®Google Scholar
• Szegő G. Zur theorie der schlichten Abbildungen. Math. Ann. 1928;100:188–211.
   Google Scholar
• Duren P. Univalent functions. New York (NY): Springer-Verlag; 1983.
   Google Scholar
• Robertson MS. The partial sums of multivalently star-like functions. Ann. Math. 1941;42:829–838.
   Google Scholar
• Ruscheweyh S. Extension of G. Szegő’s theorem on the sections of univalent functions. SIAM J. Math. Anal. 1988;19:1442–1449.
   Web of Science ®Google Scholar
• Obradović M, Ponnusamy S. Starlikeness of sections of univalent functions. Rocky Mountain J. Math. Forthcoming 2014.
   Web of Science ®Google Scholar
• Obradović M, Ponnusamy S. Univalence and starlikeness of sections of a class of univalent functions. Contemp. Math. 2013;591:195–203.
   Google Scholar
• Padmanabhan KS, Parvatham R. On the univalence and convexity of partial sums of a certain class of analytic functions whose derivatives have positive real part. Indian J. Math. 1974;16:67–77.
   Google Scholar
• Silverman H. Radii problems for sections of convex functions. Proc. Amer. Math. Soc. 1988;104:1191–1196.
   Web of Science ®Google Scholar
• Li L, Ponnusamy S. Injectivity of sections of univalent harmonic mappings. Nonlinear Anal. 2013;89:276–283.
   Web of Science ®Google Scholar
• Li L, Ponnusamy S. Disk of convexity of sections of univalent harmonic functions. J. Math. Anal. Appl. 2013;408:589–596.
   Web of Science ®Google Scholar
• Li L, Ponnusamy S. Injectivity of sections of convex harmonic mappings. Preprint.
   Google Scholar
• Avci Y, Złotkiewicz E. On harmonic univalent mappings. Ann. Univ. Mariae Curie Skłodowska (Sect A). 1990;44:1–7.
   Google Scholar
• Goodman AW. Univalent functions and nonanalytic curves. Proc. Amer. Math. Soc. 1957;8:588–601.
   Google Scholar
• Ruscheweyh S. Neighborhoods of univalent functions. Proc. Amer. Math. Soc. 1981;18:521–528.
   Google Scholar
• Qiao J, Wang X. On p-harmonic univalent mappings (in Chinese). Acta Math. Sci. 2012;32A:588–600.
   Google Scholar
• Fait M, Krzyż J, Zygmunt J. Explicit quasiconformal extensions for some classes of univalent functions. Comment. Math. Helv. 1976;51:279–285.
   Web of Science ®Google Scholar
• Pommerenke C. Univalent functions. Göttingen: Vandenhoeck and Ruprecht; 1975.
   Google Scholar
• Bharanedhar V, Ponnusamy S. Coefficient conditions for harmonic univalent mappings and hypergeometric mappings. arXiv:1109.0925v2.
   Google Scholar
• Robertson MS. On the theory of univalent functions. Ann. Math. 1936;37:374–408.
   Google Scholar
• Klein M. Functions starlike of order α. Trans. Amer. Math. Soc. 1968;131:99–106.
   Web of Science ®Google Scholar
• Ponnusamy S, Sahoo SK, Yanagihara H. Radius of convexity of partial sums of functions in the close-to-convex family. Nonlinear Anal. 2014;95:219–228.
   Web of Science ®Google Scholar
• Ma WC, Minda D. A unified treatment of some special classes of univalent functions. In: Proceedings of the conference on complex analysis, Tianjin, China, Int. Press. Conf. Proc. Lect. Notes Anal. I; 1994. p. 157–169.
   Google Scholar
• Sheil-Small T. Constants for planar harmonic mappings. J. London Math. Soc. 1990;42A:237–248.
   Google Scholar