Univalent logharmonic ring mappings
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- by Zayid Abdulhadi, Walter Hengartner and Jan Szynal PDF
- Proc. Amer. Math. Soc. 119 (1993), 735-745 Request permission
Abstract:
Univalent logharmonic ring mappings are characterized in terms of univalent starlike mappings. An existence and uniqueness theorem is also given.References
- Z. Abdulhadi and D. Bshouty, Univalent functions in $H\cdot \overline H(D)$, Trans. Amer. Math. Soc. 305 (1988), no. 2, 841–849. MR 924779, DOI 10.1090/S0002-9947-1988-0924779-4
- Z. Abdulhadi and W. Hengartner, Spirallike logharmonic mappings, Complex Variables Theory Appl. 9 (1987), no. 2-3, 121–130. MR 923213, DOI 10.1080/17476938708814256
- L. E. Dundučenko, Certain extremal properties of analytic functions given in a circle and in a circular ring, Ukrain. Mat. Ž. 8 (1956), 377–395 (Russian). MR 0085347
- Walter Hengartner and Glenn Schober, Curvature estimates for some minimal surfaces, Complex analysis, Birkhäuser, Basel, 1988, pp. 87–100. MR 981404
- W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), no. 1, 1–31. MR 869396, DOI 10.1090/S0002-9947-1987-0869396-9
- Walter Hengartner and Glenn Schober, Univalent harmonic exterior and ring mappings, J. Math. Anal. Appl. 156 (1991), no. 1, 154–171. MR 1102603, DOI 10.1016/0022-247X(91)90388-G
- Yûsaku Komatu, On analytic functions with positive real part in an annulus, K\B{o}dai Math. Sem. Rep. 10 (1958), 84–100. MR 97531
- Yûsaku Komatu, On the range of analytic functions with positive real part, K\B{o}dai Math. Sem. Rep. 10 (1958), 145–160. MR 107011
- A. E. Livingston and J. A. Pfaltzgraff, Structure and extremal problems for classes of functions analytic in an annulus, Colloq. Math. 43 (1980), no. 1, 161–181 (1981). MR 615984, DOI 10.4064/cm-43-1-161-181
- Han Nishimiya, On coefficient-regions of Laurent series with positive real part, K\B{o}dai Math. Sem. Rep. 11 (1959), 25–39. MR 108594
- Johannes C. C. Nitsche, Mathematical Notes: On the Module of Doubly-Connected Regions Under Harmonic Mappings, Amer. Math. Monthly 69 (1962), no. 8, 781–782. MR 1531840, DOI 10.2307/2310779 —, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin, 1975.
- V. A. Zmorovič, On some classes of analytic functions univalent in a circular ring, Mat. Sbornik N.S. 32(74) (1953), 633–652 (Russian). MR 0055448
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 735-745
- MSC: Primary 30C55
- DOI: https://doi.org/10.1090/S0002-9939-1993-1195710-1
- MathSciNet review: 1195710