Criteria of univalence and fully –accessibility for p–harmonic and p–analytic functions

References

• Balk MB. Polyanalytic functions and their generalizations. Berlin: Springer; 1997 Chapter in complex analysis I. (Encyclopaedia of mathematical sciences: 85); p. 195–253.
   Google Scholar
• Chen Sh, Ponnusamy S, Wang X. Bloch constant and Landau’s theorem for planar p-harmonic mappings. J Math Anal Appl. 2011;373(1):102–110.
   Web of Science ®Google Scholar
• Li P, Ponnusamy S, Wang X. Some properties of planar p-harmonic and log-p-harmonic mappings. Bull Malays Math Sci Soc. 2013;36(3):595–609.
   Web of Science ®Google Scholar
• Olofsson A. Differential operators for a scale of Poisson type kernels in the unit disc. J Anal Math. 2014;123:227–249.
   Web of Science ®Google Scholar
• Borichev A, Hedenmalm H. Weighted integrability of polyharmonic functions. Adv Math. 2014;264:464–505.
   Web of Science ®Google Scholar
• Chen Sh, Vuorinen M. Some properties of a class of elliptic partial differential operators. J Math Anal Appl. 2015;431:1124–1137.
   Web of Science ®Google Scholar
• Chen Sh, Ponnusamy S, Wang X. On some properties of solutions of the p-harmonic equation. Filomat. 2013;27:577–591.
   Web of Science ®Google Scholar
• Chen Sh, Ponnusamy S, Wang X. Landau’s theorem for p-harmonic mappings in several variables. Ann Polon Math. 2012;103:67–87.
   Web of Science ®Google Scholar
• Duren P. Harmonic mappings in the plane. Cambridge, UK: Cambridge University Press; 2004.
   Google Scholar
• Clunie JG, Sheil-Small T. Harmonic univalent functions. Ann Acad Sci Fenn Ser A. 1984;I(9):3–25.
   Google Scholar
• Ponnusamy S, Qiao J. Polynomial approximation of certain biharmonic mappings. Nonlinear Anal. 2013;81:149–158.
   Web of Science ®Google Scholar
• Starkov VV. Univalence of harmonic functions, the problem of Ponnusamy and Sairam, and constructions of univalent polynomials. Prob Anal Issues Anal. 2014;3(21)(2):59–73.
   Google Scholar
• Bazilevich IE. The problem of coefficients of univalent functions. Math J Aviat Inst [Moscow]. 1945;29–47. Russian.
   Google Scholar
• Abdulhadi Z, El Hajj L. Univalent biharmonic mappings and linearly connected domains. Int J Anal Appl. 2015;9(1):1–8.
   Google Scholar
• Adams RA, Fournier J. Cone conditions and properties of Sobolev spaces. J Math Anal Appl. 1977;61:713–734.
   Web of Science ®Google Scholar
• Besov OV, Ilin VP, Nikolskij SM. Integral representations of functions and imbedding theorems. Vol. 1-2, New York (NY): Wiley; 1978/1979.
   Google Scholar
• Dolženko EP. Boundary properties of arbitrary functions. Math USSR Izv. 1967;1(1):1–12.
   Google Scholar
• Zaremba S. Sur le principe de Dirichlet. Acta Math. 1911;34:293–316.
   Google Scholar
• Hazewinkel M. Encyclopaedia of mathematics. Vol. 2 (C), Dordrecht: Kluwer; 1988.
   Google Scholar
• Liczberski P, Starkov VV. Domains in ℝn with conical accessible boundary. J Math Anal Appl. 2013;408(2):547–560.
   Web of Science ®Google Scholar
• Amozova KF. Necessary and sufficient conditions of (α,β)-accessibility of domain in nonsmooth case. Prob Anal Issues Anal. 2015;4(22)(2):3–11.
   Google Scholar
• Amozova KF. Sufficient conditions of α-accessibility of domain in nonsmooth case. Prob Anal Issues Anal. 2013;2(20)(1):3–13.
   Google Scholar
• Amozova KF, Ganenkova EG. About planar (α,β)-accessible domains. Prob Anal Issues Anal. 2014;3(21)(2):3–15.
   Google Scholar
• Amozova KF, Ganenkova EG. On α-accessible domains. Vestnik St Petersburg Univ Math. 2015;48(4):195–203.
   Google Scholar
• Amozova KF, Starkov VV. α-accessible domains, a nonsmooth case. Izv Sarat Univ N S Ser Math Mech Inform. 2013;13(3):3–8.
   Google Scholar
• Anikiev AN. Plane domains with special cone condition. Prob Anal Issues Anal. 2014;3(21)(2):16–31.
   Google Scholar
• Stankiewicz J. Quelques problèmes extrémaux dans les classes α-angulairement étoilées [Some extremal problems in classes of α-angular-starlike functions]. Ann Univ Mariae Curie-Skłodowska. 1966;20:59–75.
   Google Scholar
• Stankiewicz J. Some remarks concerning starlike functions, Bulletin de l’academie Polonaise des sciences. Série Scie Math Astr Phys. 1970;18(3):143–146.
   Google Scholar
• Brannan DA, Kirwan WE. On some classes of bounded univalent functions. J London Math Soc. 1969;2(1):431–443.
   Google Scholar
• Chuaqui M, Duren P, Osgood B. Curvature properties of planar harmonic mappings. Comput Methods Funct Theory. 2004;4(1):127–142.
   Google Scholar
• Ahlfors LV. Lectures on quasiconformal mappings. Am Math Soc Univ Lecture Ser. 2006;38:164p.
   Google Scholar
• Sugawa T. A self-duality of strong starlikeness. Kodai Math J. 2005;28:382–389.
   Google Scholar