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Residues and Argument Principle for A(z)-Analytic Functions

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Abstract

In this paper, we obtain formulas for residues and prove analogs of the argument principle

and Rouche theorems for A(z)-analytic functions.

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References

  1. L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, Princeton etc. (1966).

    MATH  Google Scholar 

  2. A. L. Buchgeim, Inversion Formulas in Inverse Problems [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  3. A. L. Buchgeim and S. G. Kazantsev, “Elliptic Beltrami-type systems and problems of tomography,” Dokl. Akad. Nauk SSSR, 315, No. 1, 15–19 (1990).

    Google Scholar 

  4. V. Gutlyanski, V. Ryazanov, U. Srebro, and E. Yakubov, The Beltrami Equation: A Geometric Approach, Springer-Verlag (2011).

  5. N. M. Jabborov and Kh. Kh. Imomnazarov, Initial-Boundary Problems of Mechanics of Two- Velocity Media [in Russian], Tashkent (2012).

  6. N. M. Jabborov and T. U. Otaboev, “Cauchy theorem for A(z)-analytic functions,” Uzbek. Mat. Zh., 1, 15–18 (2014).

    MathSciNet  Google Scholar 

  7. N. M. Jabborov and T. U. Otaboev, “An analog of the Cauchy integral formula for A-analytic function,” Uzbek. Mat. Zh., 4, 50–59 (2016).

    Google Scholar 

  8. M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of a Complex Vvariable, Nauka, Moscow (1987).

    Google Scholar 

  9. A. Sadullaev and N. M. Jabborov, “On a class of A-analytic functions,” Zh. Sib. Fed. Univ. Ser. Math. Phys., 9, No 3, 374–383 (2016).

    Article  Google Scholar 

  10. I. N. Vekua, Generalized Analytic Functions, Pergamon Press, Oxford (1962).

    MATH  Google Scholar 

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Authors and Affiliations

  1. National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan

    Zh. K. Tishabaev, T. U. Otaboev & Sh. Ya. Khursanov

Authors
  1. Zh. K. Tishabaev
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  2. T. U. Otaboev
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  3. Sh. Ya. Khursanov
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Corresponding author

Correspondence to T. U. Otaboev.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 144, Proceedings of the Conference “Problems of Modern Topology and Its Applications” (May 11–12, 2017), Tashkent, Uzbekistan, 2018.

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Tishabaev, Z.K., Otaboev, T.U. & Khursanov, S.Y. Residues and Argument Principle for A(z)-Analytic Functions. J Math Sci 245, 350–358 (2020). https://doi.org/10.1007/s10958-020-04696-2

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  • DOI: https://doi.org/10.1007/s10958-020-04696-2

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