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Starlikeness of functions with bounded mean modulus

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Literature Cited

  1. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Gosudarstvennoe Izd. Tekhnikoteoreticheskoi Literaturey, Moscow-Leningrad (1950).

    Google Scholar 

  2. G. M. Goluzin, “Estimate of the derivative for functions that are regular and bounded in the disk,” Mat. Sb.,16, No. 3, 295–306 (1945).

    Google Scholar 

  3. V. P. Vazhdaev and S. A. Gel'fer, “Certain estimates in the class of analytic functions of bounded form,” Mat. Sb.,84, No. 2, 273–289 (1971).

    Google Scholar 

  4. L. V. Kresnyakova, “On analytic functions with bounded mean modulus,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 98–103 (1961).

    Google Scholar 

  5. L. V. Kresnyakova, “On regular functions with bounded mean modulus,” Dokl. Akad. Nauk SSSR,147, No. 2, 290–293 (1962).

    Google Scholar 

  6. L. V. Kresnyakova, “On the radii of starlikeness and convexity for functions with bounded mean modulus,” Izv. Akad. Nauk Arm. SSR, Ser. Fiz.-Mat.,14, No. 4, 49–55 (1961).

    Google Scholar 

  7. V. P. Vazhdaev, “Application of L. S. Pontryagin's maximum principle to the solution of extremal problems in the class of the functions with bounded mean modulus,” Sib. Mat. Zh.,21, No. 3, 42–55 (1980).

    Google Scholar 

  8. S. Ya. Khavinson, “On the radii of univalence, starlikeness, and convexity of a class of analytic functions in multiply connected domains,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 233–240 (1958).

    Google Scholar 

  9. G. Ts. Tumarkin and S. Ya. Khavinson, “Classes of analytic functions in multiply connected domains,” in: Investigations in Modern Problems of Theory of Functions of a Complex Variable [in Russian], Gosudarstvennoe Izd. Fizikomatematicheskoi Literatury, Moscow (1960), pp. 45–77.

    Google Scholar 

  10. S. Ya. Khavinson, “On the representation of extremal functions in the classes Eq by the Green and the Neumann functions,” Mat. Zametki,16, No. 5, 707–716 (1974).

    Google Scholar 

  11. G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  12. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  13. G. Pólya and G. Szegö, Problems and Theorems in Analysis [Russian translation], Vol. 2, Nauka, Moscow (1978).

    Google Scholar 

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Gorky. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 2, pp. 14–22, March–April, 1986.

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Vazhdaev, V.P. Starlikeness of functions with bounded mean modulus. Sib Math J 27, 154–161 (1986). https://doi.org/10.1007/BF00969380

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  • DOI: https://doi.org/10.1007/BF00969380

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