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Original Articles

On a subclass of close-to-convex harmonic mappings

, &
Pages 1627-1643 | Received 27 Oct 2015, Accepted 10 May 2016, Published online: 13 Jun 2016

References

  • Duren P. Harmonic mappings in the plane. Cambridge: Cambridge University Press; 2004.
  • Clunie J, Sheil-Small T. Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A. I Math. 1984;9:3–25.
  • Ponnusamy S, Rasila A. Planar harmonic and quasiregular mappings. Top. Mod. Funct. Theory. Ramanujan Math. Soc. Lect. Notes Ser. 2013;19:267–333. Ramanujan Math. Soc., Mysore.
  • Suffridge TJ. Some special classes of conformal mappings. In: Kühnau R, editor. Handbook of complex analysis: geometric function theory. Amsterdam: Elsevier; 2005; vol. 2. p. 309–338.
  • Fekete M, Szegő G. Eine Bemerkung über ungerade schlichte Funktionen [A remark on odd schlicht functions.]. J. London Math. Soc. 1933;8:85–89.
  • Abdel H, Gawad D, Thomas K. The Fekete-Szegő problem for strong close-to-convex functions. Proc. Am. Math. Soc. 1992;114:345–349.
  • Koepf W. On the Fekete-Szegö problem for close-to-convex functions. Proc. Am. Math. Soc. 1987;101:89–95.
  • Koepf W. On the Fekete-Szegö problem for close-to-convex functions II. Arch. Math. 1987;49:420–433.
  • Szegö G. Zur Theorie der schlichten Abbildungen [On the theory of univalent analytic functions]. Math. Ann. 1928;100:188–211.
  • Robertson MS. The partial sums of multivalently star-like functions. Ann. Math. 1941;42:829–838.
  • Ruscheweyh S. Extension of G. Szegö’s theorem on the sections of univalent functions. SIAM J. Math. Anal. 1988;19:1442–1449.
  • 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.
  • Chen J, Rasila A, Wang X. Coefficient estimates and radii problems for certain classes of polyharmonic mappings. Complex Var. Elliptic Equ. 2015;60:354–371.
  • Li L, Ponnusamy S. Injectivity of sections of univalent harmonic mappings. Nonlinear Anal. 2013;89:276–283.
  • Li L, Ponnusamy S. Disk of convexity of sections of univalent harmonic functions. J. Math. Anal. Appl. 2013;408:589–596.
  • Li L, Ponnusamy S. Sections of stable harmonic convex functions. Nonlinear Anal. 2015;123–124:178–190.
  • Mocanu PT. Injectivity conditions in the complex plane. Complex Appl. Oper. Theory. 2011;5:759–766.
  • Mocanu PT. Sufficient conditions of univalence for complex functions in the class C∑. Rev. Anal. Numér. Théor. Approx. 1981;10:75–79.
  • Bshouty D, Lyzzaik A. Close-to-convexity criteria for planar harmonic mappings. Complex Appl. Oper. Theory. 2011;5:767–774.
  • Bharanedhar SV, Ponnusamy S. Coefficient conditions for harmonic univelent mappings and hypergeometric mappings. Rocky Mountain J. Math. 2014;44:753–777.
  • Nagpal S, Ravichandran V. Starlikeness, convexity and close-to-convexity of harmonic mappings. Current topics in pure and computational complex analysis: Trends in Mathematics. New Delhi: Birkhäuser/Springer; 2014. p. 201–214. Available from:http://arxiv.org/abs/1207.3404.
  • Bshouty D, Joshi SS, Joshi SB. On close-to-convex harmonic mappings. Complex Var. Elliptic Equ. 2013;58:1195–1199.
  • Hayami T. Coefficient conditions for harmonic close-to-convex functions. Abstr. Appl. Anal. 2012, 2012: Article ID 413965, 12 p. doi:10.1155/2012/413965.
  • Kalaj D. Quasiconformal harmonic mappings and close-to-convex domains. Filomat. 2010;24:63–68.
  • Kalaj D, Ponnusamy S, Vuorinen M. Radius of close-to-convexity and fully starlikeness of harmonic mappings. Complex Var. Elliptic Equ. 2014;59:539–552.
  • Nagpal S, Ravichandran V. A subclass of close-to-convex harmonic mappings. Complex Var. Elliptic Equ. 2014;59:204–216.
  • Ponnusamy S, Kaliraj AS. On harmonic close-to-convex functions. Comput. Methods Funct. Theory. 2012;12:669–685.
  • Ponnusamy S, Kaliraj AS. Constants and characterization for certain classes of univalent harmonic mappings. Mediterr. J. Math. 2015;12:647–665.
  • Avci Y, Złotkiewicz E. On harmonic univalent mappings. Ann. Univ. Mariae Curie Skłodowska (Sect A). 1990;44:1–7.
  • Li L, Ponnusamy S. Generalized Zalcman conjecture for convex functions of order -1/2. J. Anal. 2014;22:77–87.
  • Pommerenke C. Univalent functions. Göttingen: Vandenhoeck and Ruprecht; 1975.
  • Goodman AW. Univalent functions. Vol. 1--2. Tampa (FL): Mariner; 1983.

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