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Elements of geometric theory for functions of quaternionic variable

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Abstract

Based on idens in the classical complex case, in this note we present some possible ways of extension of the classical geometric function theory to functions of quaternlonic variables. An univalence result is obtained and certain kinds of starlikeness and of convexity are studied.

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References

  1. Al-Amiri H. and P. T. Mocanu, Spirallike nonanalytic functions,Proc. Amer. Math. Soc.,82, 1, 61–65 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  2. Birman G. S., “Pseudoquaternions and unitary null curves”, Instituto Argentino de Matematica-Conicet, Preprint No.257, ISSN 0325-6677 (1985).

  3. Bracks F., R. Delanghe and S. Sommer, Clifford Analysis,Research Notes in Mathematics, 76, Pitman Adv. Publ. Program, Boston (1982).

    Google Scholar 

  4. Fueter R., Analytische Funktionen einer Quaternionenvariablen,Comment. Math. Helv. 4, 9–20 (1932).

    Article  MathSciNet  Google Scholar 

  5. Kohr G., Certain sufficient conditions of univalency for complex mappings in the classC 2 on ℂn,Stud. Cerc. Mat.,48 (5-6), 349–356 (1996).

    MATH  MathSciNet  Google Scholar 

  6. Lugojan S., Quaternionic derivability,Anal. Univ. Timisoara, ser. Ştiinţ. Mat., vol. XXIX, fasc. 2–3, 175–190 (1991).

    MathSciNet  Google Scholar 

  7. Lugojan S., Quaternionic derivability, II, “Proceed. Meeting on Quaternionic Structures in Mathematics and Physics”, Trieste, 1994; SISA-Trieste, p. 217–224 (1996).

  8. Lugojan S., About the symmetry of the quaternionic derivatives, Bull. Şttinţ. Univ. “Politehnica”. Timişoara, tom42(56) fasc. 1, 7–11 (1997).

    MathSciNet  Google Scholar 

  9. Mejlihzon A. S., “On the notion of monogenic quaternions” (in Russian).Dokl. Akad. Mauk SSSR 59 3, 431–434 (1948).

    Google Scholar 

  10. Mocanu P. T., Sufficiont conditions of univalency for complex functions in the classC 1.Rev. Anal. Numér. Théor. Approx. 10, 1, 75–79 (1981).

    MATH  MathSciNet  Google Scholar 

  11. Mocanu P. T., Starlikeness and convexity for non-analytic functions in the unit disc,Mathenatica (Cluj),22 (45) 1, 77–83 (1980).

    MathSciNet  Google Scholar 

  12. Mocann P. T., Alpha-convex nonanalytic functions,Mathematica (Cluj),29 (52) 1, 49–55 (1987).

    MathSciNet  Google Scholar 

  13. Moisil Gr. C., Sur les quaternions monogènes.Bull. Sci. Math. (Paris)LV 168–174, (1931).

    Google Scholar 

  14. Sudbery A., Quaternionic analysis,Math. Proc. Cambridge Philos, Soc.,85, 199–225 (1979).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Yaglom I. M., “Complex Numbers in Geometry”, Academic Press, New York and London, (1968).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Oradea, Str. Armatei Române 5, 3700, Oradea, Romania

    Sorin G. Gal

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  1. Sorin G. Gal
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Correspondence to Sorin G. Gal.

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Gal, S.G. Elements of geometric theory for functions of quaternionic variable. AACA 10, 91–106 (2000). https://doi.org/10.1007/BF03042011

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  • DOI: https://doi.org/10.1007/BF03042011

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