Submultiplicative properties of the φK-distortion function
Qiu, S.-L. ; Vuorinen, M.
Studia Mathematica, Tome 119 (1996), p. 225-242 / Harvested from The Polish Digital Mathematics Library

Some inequalities related to the submultiplicative properties of the distortion function φK(r) are derived.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216253
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     title = {Submultiplicative properties of the $$\phi$\_{K}$-distortion function},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {225-242},
     zbl = {0848.30012},
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Qiu, S.-L.; Vuorinen, M. Submultiplicative properties of the $φ_{K}$-distortion function. Studia Mathematica, Tome 119 (1996) pp. 225-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv117i3p225bwm/

[00000] [AQV] G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy, Sharp inequalities for elliptic integrals, Report Series No. 302, Univ. of Auckland, 1994.

[00001] [AVV1] G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Distortion functions for plane quasiconformal mappings, Israel J. Math. 62 (1988), 1-16. | Zbl 0652.30013

[00002] [AVV2] G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Special functions of quasiconformal theory, Exposition. Math. 7 (1989), 97-136. | Zbl 0686.30015

[00003] [AVV3] G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Functional inequalities for complete elliptic integrals and their ratios, SIAM J. Math. Anal. 21 (1990), 536-549. | Zbl 0692.33001

[00004] [AVV4] G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Functional inequalities for hypergeometric functions and complete elliptic integrals, ibid. 23 (1992), 512-524. | Zbl 0764.33009

[00005] [AVV5] G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Inequalities for plane quasiconformal mappings, in: The Mathematical Heritage of Wilhelm Magnus-Groups, Geometry & Special Functions, W. Abikoff, J. S. Birman and K. Kuiken (eds.), Contemp. Math. 169, Amer. Math. Soc., Providence, R.I., 1994, 1-27.

[00006] [B] B. C. Berndt, Ramanujan Notebooks. Part III, Springer, New York, 1991.

[00007] [BB] J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, New York, 1987.

[00008] [Bo] F. Bowman, Introduction to Elliptic Integrals with Applications, Dover, New York, 1961.

[00009] [BF] P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Springer, Berlin, 1954.

[00010] [C] B. C. Carlson, Special Functions of Applied Mathematics, Academic Press, New York, 1977. | Zbl 0394.33001

[00011] [Fr] C.-E. Fröberg, Complete Elliptic Integrals, CWK Gleerup, Lund, 1957.

[00012] [He] C.-Q. He, Distortion estimates of quasiconformal mappings, Sci. Sinica Ser. A 27 (1984), 225-232.

[00013] [K] R. Kühnau, Eine Methode, die Positivität einer Funktion zu prüfen, Z. Angew. Math. Mech. 74 (1994), 140-142.

[00014] [LV] O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Grundlehren Math. Wiss. 126, 2nd ed., Springer, New York, 1973. | Zbl 0267.30016

[00015] [M] G. J. Martin, The distortion theorem for quasiconformal mappings, Schottky's theorem and holomorphic motions, Math. Research Report No. MRR 045-94, The Australian National Univ., 1994.

[00016] [P1] D. Partyka, An alternative proof of a result due to Douady and Earle, Ann. Univ. Mariae Curie-Skłodowska 42 (1988), 59-68. | Zbl 0712.30040

[00017] [P2] D. Partyka, Approximation of the Hersch-Pfluger distortion function, Ann. Acad. Sci. Fenn. AI 18 (1993), 343-354. | Zbl 0793.30013

[00018] [Q1] S.-L. Qiu, Distortion properties of K-qc. maps and a better estimate of Mori's constant, Acta Math. Sinica 35 (1992), 492-504. | Zbl 0778.30021

[00019] [Q2] S.-L. Qiu, Proof of a conjecture on the first elliptic integrals, J. Hangzhou Inst. Electronics Engrng. 3 (1993), 29-36.

[00020] [QV] S.-L. Qiu and M. K. Vamanamurthy, Sharp estimates for complete elliptic integrals, SIAM J. Math. Anal., to appear. | Zbl 0860.33014

[00021] [QVV1] S.-L. Qiu, M. K. Vamanamurthy and M. Vuorinen, Inequalities for distortion functions and quasiconformal mappings, manuscript, 1994.

[00022] [QVV2] S.-L. Qiu, M. K. Vamanamurthy and M. Vuorinen, Sharp inequalities for Hersch-Pfluger distortion function, Preprint 93, Nov. 1995, Dept. Math., University of Helsinki. | Zbl 0946.30010

[00023] [VV] M. K. Vamanamurthy and M. Vuorinen, Functional inequalities, Jacobi products, and quasiconformal maps, Illinois J. Math. 38 (1994), 394-419. | Zbl 0799.30011

[00024] [Vu1] M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math. 1319, Springer, 1988.

[00025] [Vu2] M. Vuorinen, Singular values, Ramanujan modular equations, and Landen transformations, manuscript 1994.

[00026] [W] C.-F. Wang, On the precision of Mori's theorem in Q-mapping, Science Record 4 (1960), 329-333. | Zbl 0103.30202

[00027] [WW] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1958.

[00028] [Z] J. Zając, The distortion function ΦK and quasihomographies, in: Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (eds.), World Sci., Singapore, 1992, 403-428. | Zbl 0985.30517