Abstract
Some families of univalent functions for which the image domain has a special geometric property were considered in the study. Among the families considered are convex and star-like mappings, close-to-convex mappings, spirallike mappings. The connection between the geometry of the image domains and analytic properties of the mapping function was described. Also geometric properties of Hadamard Product of geometric functions were collected.
References
- S. Ruscheweyh, Convolution In Geometric Function Theory, Presses de l'Université de Montréal, Montréal, (1982)
- P.L. Duren, Univalent Functions, Springer, New York, (1983)
- Z. Nehari, Conformal mapping, Mc. Graw-Hill, (1952)
- G. Schober, Univalent Functions-Selected Topics, Springer, Berlin-Heidelberg, (1975)
- G. P 4́lya, I.J. Schoenberg , Pacific J. Math. 8 (1958) 295-334.
- T.J. Suffridge, J. Math. Mech. 15 (1966) 795-804.
- S. Ruscheweyh, Sheil-Small T., Comment Math. Helv. 48 (1973) 119-135.
- T.J. Suffridge, Duke Math. J. 37 (1970) 775-777.
- T. Sheil-Small, J. London Math. Soc. 1 (1969) 483-492.
- Ch. Pommerenke, J. London Math. Soc. 37 (1962) 209-224.
- J.R. Prather, Complex Variables Vol. 41 (1998) 17-26.
- H. Silverman, E.M. Silvia, D. Telage, Mathematische Zeitschrift (1918) 125-130.
- S. Ruscheweyh, Comment Math. Helv. 52 (1977) 497-509 .
- L. “pa {̆ek, •“asopis P ̆st Mat.-Fys. 62 (1933) 12-19.
- S. Ruscheweyh, Proc. Amer. Math. Soc. 49 (1975) 109-115.
- S. Owa, S. Fukuı, K. Sakaguchı, S. Ogawa, Internat. J. Math. & Math. Sci., Vol.9(4) (1986) 7217
- R.W. Barnard, C. Kellog, Michigan Math. J. 27 (1978)
- Z. Shareef, S. Hussain, M. Darus, Journal of Inequalities and Applications 2012 (2012) 213 J.W. Alexander, Ann. Math. 17 (1915) 12-22.
- R. Roy, Sources in the Development of Mathematics, Cambridge University Press (2011).
Abstract
Bu çalışmada görüntü kümesi özel bir geometrik özelliğe sahip olan ünivalent fonksiyonların bazı aileleri incelenmiştir. Bu aileler konveks ve yıldızıl dönüşümler, hemen hemen konveks dönüşümler ve spiral-like dönüşümlerdir. Bu fonksiyonların analitik özellikleri ile görüntü kümesinin geometrisi arasındaki bağlantı ifade edilmiştir. Ayrıca bu fonksiyonların Hadamard Çarpımının geometrik özellikleri ve bu çarpım ile oluşturulan koşullar derlenmiştir.
References
- S. Ruscheweyh, Convolution In Geometric Function Theory, Presses de l'Université de Montréal, Montréal, (1982)
- P.L. Duren, Univalent Functions, Springer, New York, (1983)
- Z. Nehari, Conformal mapping, Mc. Graw-Hill, (1952)
- G. Schober, Univalent Functions-Selected Topics, Springer, Berlin-Heidelberg, (1975)
- G. P 4́lya, I.J. Schoenberg , Pacific J. Math. 8 (1958) 295-334.
- T.J. Suffridge, J. Math. Mech. 15 (1966) 795-804.
- S. Ruscheweyh, Sheil-Small T., Comment Math. Helv. 48 (1973) 119-135.
- T.J. Suffridge, Duke Math. J. 37 (1970) 775-777.
- T. Sheil-Small, J. London Math. Soc. 1 (1969) 483-492.
- Ch. Pommerenke, J. London Math. Soc. 37 (1962) 209-224.
- J.R. Prather, Complex Variables Vol. 41 (1998) 17-26.
- H. Silverman, E.M. Silvia, D. Telage, Mathematische Zeitschrift (1918) 125-130.
- S. Ruscheweyh, Comment Math. Helv. 52 (1977) 497-509 .
- L. “pa {̆ek, •“asopis P ̆st Mat.-Fys. 62 (1933) 12-19.
- S. Ruscheweyh, Proc. Amer. Math. Soc. 49 (1975) 109-115.
- S. Owa, S. Fukuı, K. Sakaguchı, S. Ogawa, Internat. J. Math. & Math. Sci., Vol.9(4) (1986) 7217
- R.W. Barnard, C. Kellog, Michigan Math. J. 27 (1978)
- Z. Shareef, S. Hussain, M. Darus, Journal of Inequalities and Applications 2012 (2012) 213 J.W. Alexander, Ann. Math. 17 (1915) 12-22.
- R. Roy, Sources in the Development of Mathematics, Cambridge University Press (2011).
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Publication Date | September 5, 2014 |
| IZ | https://izlik.org/JA25FM26SL |
| Published in Issue | Year 2014 Volume: 2 Issue: 1 |