Literature Cited
N. A. Lebedev, The Area Principle in the Theory of Single-Sheeted Functions [in Russian], Nauka, Moscow (1975).
A. Z. Grinshpan and Z. D. Kolomoitseva, “The area method for functions with no common values,” Vestn. Leningr. Univ., Ser. Mat., Mekh. Astron., No. 19, 31–36 (1979).
I. M. Milin, Single-Sheeted Functions and Orthonormed Systems [in Russian], Nauka, Moscow (1971).
O. Lehto, “Schlicht functions with a quasiconformal extension,” Ann. Acad. Sci. Fenn. Suomolais Tiedeakat. Toimituks, Ser. AI,500, 10 (1971).
R. Kühnau, “Verzuerrungssätze und Koeffizientenbedingungen von Grunsky'schen Typ für quasikonforme Abbildungen,” Math. Nachr.,48, 77–105 (1971).
V. Ya. Gutlyanskii, “On the area principle for a class of quasiconformal mappings,” Dokl. Akad. Nauk SSSR,212, No. 3, 540–543 (1973).
V. G. Sheretov, “On a variant of the area theorem,” Matematicheskii Analiz, Krasnodar,217, No. 3, 77–80 (1976).
V. A. Shchepetev, “An area theorem for a class of quasiconformal mappings,” in: Extremal Problems in Function Theory [in Russian], Tomsk (1979), pp. 69–85.
G. E. Shilov and B. L. Gurevich, Integral, Measure, and Derivative [in Russian], Nauka, Moscow (1967).
L. Ahlfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).
S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc. (1969).
D. Aharonov, “A generalization of a theorem of J. A. Jenkins,” Math. Z.,110, 218–222 (1969).
A. Z. Grinshpan, “An application of the area principle to Biberbach-Eulenberg functions,” Mat. Zametki,11, No. 6, 609–618 (1972).
R. Kühnau, “Zu den Grunskyschen Coeffizientenbedingungen,”, Ann. Acad. Sci. Fenn., Ser. A1,6, 125–130 (1981).
L. V. Ahlfors, “Remarks on the Neumann-Poincare integral equation,”, Pac. J. Math.,2, 271–280 (1952).
S. L. Krushkal', “A remark on the domain of values of analytic functionals on classes of conformal and quasiconformal mappings,” Sib. Mat. Zh.,23, No. 4, 90–98 (1982).
A. Z. Grinshpan, “On the growth of the coefficients of single-sheeted functions with quasiconformal continuation,” Sib. Mat. Zh.,23, No. 2, 208–211 (1982).
D. Horowitz, “A further refinement for coefficient estimates of univalent functions,” Proc. Am. Math. Soc.,71, No. 2, 217–221 (1978).
A. Z. Grinshpan, “An improved estimate for the difference in modulus of the coefficients of single-sheeted functions,” in: Some Problems in Contemporary Function Theory [in Russian], Novosibirsk (1976), pp. 41–45.
A. Z. Grinshpan, “On the coefficients of powers of single-sheeted functions,”, Sib. Mat. Zh.,22, No. 4, 88–93 (1981).
S. A. Gel'fer, “A class of regular functions which do not take any pair of values w and-w,” Mat. Sb.,19 (61), No. 1, 33–46 (1946).
A. E. Grinshpan, “On the coefficients of single-sheeted functions which do not take any pair of values w and-w,” Mat. Zametki,11, No. 1, 3–14 (1972).
J. A. Hummel, “A variational method for Gel'fer functions,” J. d'Anal. Math.,30, 271–280 (1976).
A. Z. Grinshpan, “On the Taylor coefficients of certain classes of single-sheeted functions,” in Metric Problems in Function Theory [in Russian], Sb. Nauch. Trudov, Naukova Dumka, Kiev (1980), pp. 28–32.
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Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 1, pp. 49–65, January–February, 1985.
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Grinshpan, A.Z. Coefficient inequalities for conformal mappings with homeomorphic continuation. Sib Math J 26, 37–50 (1985). https://doi.org/10.1007/BF00968961
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DOI: https://doi.org/10.1007/BF00968961