ON A CLASS OF FUNCTIONS OF COMPLEX ORDER

Article Sidebar

PDF
Published: Jun 1, 1999
DOI: https://doi.org/10.5556/j.tkjm.30.1999.4221
Keywords:
Univalent functions, starlike of complex order, functions of complex order, integral operator

Main Article Content

S. ABDUL HALIM
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia.

Abstract




Denote by $\mathcal{R} (b)$, the class of normalized analytic functions f which satisfies $\text{Re}(1 十 \frac{1}{b}(f'(z)-1)) >0$, for $z\in D =\{z:|z|<1\}$ and $b$ a non-zero complex number. In this paper, some results concerning functions belonging to this class are being considered.




Article Details

How to Cite
HALIM, S. A. (1999). ON A CLASS OF FUNCTIONS OF COMPLEX ORDER. Tamkang Journal of Mathematics, 30(2), 147–153. https://doi.org/10.5556/j.tkjm.30.1999.4221
Issue
Vol. 30 No. 2 (1999)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. 17(1915), 12-22.

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc 135(1969), 429-446.

P. L. Duren, Univalent Functions, Springer-Verlag, Berlin, 1983.

A. W. Goodman, Univalent Functions, Vol. I, II, Polygonal Publishing House, Washington, 1983.

D. J. Hallenbeck, Convex hulls and extreme points of some families of univalent functions, Trans. Amer. Math. Soc. 192(1974), 285-292.

F. R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic func­tions, Proc. Amer. Math. Soc. 20(1969), 8-12.

R. J. Libera, some classes of regular univalent functions, Proc. Amer. Maths. Soc. 16(1965), 755-758.

T. H. Macgregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc. 9(1962), 532-537.

S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65(1978), 289-305.

S. S. Miller, P. T. Mocanu and M. O. Reade, Starlike integral operators, Pacific J. Math. 79(1978), 157-168.

P. T. Mocanu, On a close-to-convexity preserving integral operator, Studia Univ. Babes­ Bolyai, Math. 32(1987), 53-56.

M. A . Nasr and M. K. Aouf, Radius of convexity for the class of starlike functions of complex order, Bull. Fac. Sci. Assiut Univ. 12(1983), 153-159.

M. A . Nasr and M. K. Aouf, Starlike functions of complex order, J. of Natural Sciences and Mathematics 25 (1985), 1- 12 .

R. Nevalinna, Uber die konforme Abbilung von Sterngebieten, Oversikt av Finska-Vetenskap Soc. Forh. 63(1921), 1-21.

H. M. Srivastava and S. Owa (Editors), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, new jersey, London and Hong Kong, 1992.

Rosihan M. Ali and D. K. Thomas, Proc. Japan A.cad. 67A (1991), 319-321.

V. Selinger, Some integral operators preserving certain geometric properties, Rev. Roumaine Math-Pures Appl.-·33(1988), 10, 889-900.