Sains Ma1aysiana 28: 141-149 (1999)                                                                                          Pengajian Kuantitatif/

                                                                                                                                                                Quantitative Studies

 

Functions of Bounded Boundary Rotation

 

Maslinda Darus

Department of Mathematics

Faculty of Mathematical Sciences, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor D.E. Malaysia

 

 

ABSTRACT

 

For k2, let Vk be the class of analytic normalised functions of bounded boundary rotation defined in the open disc D by

 

 

with z = re For  and given by , sharp bounds are obtained for the functional  when μ is real.

 

ABSTRAK

 

Untuk k2, katalah Vk kelas fungsi analisis temormal dengan putaran sempadan terbatas yang tertakrif di dalam cakera terbuka D oleh

 

 

dengan z = re. Untuk dan , batas atas terbaik diperoleh untuk fungsian apabila μ adalah nyata.

 

 

RUJUKAN/REFERENCES

 

Abdel-Gawad, H.R. & Thomas, D.K. 1992. The Fekete-Szego problem for strongly close-to-convex functions. Proc. Amer. Math. Soc. 114: 345-349.

Lowner, K. 1917. Untersuchungen tiber die verzerrung die konformen abbildungen des einheitskreises , verschwindender ableifert geleifert werden. Ber. Verh. Sachs. Ges. Wiss. Leipzig. 69: 89-106

Lehto, O. 1952. On the distortion of conformal mappkings with bounded boundary rotation. Ann. Acad. Sci. Fennicae.

Paatero, V. 1931. Uber die konforme Abbildung von gebieten deren rander von beschrankter drehrung sind. Ann. Acad. Sci. Fenn. Ser. 9: 1-77.

Paatero, V. 1933. Uber gebieten von beschrankter randdrehrung. Ann. Acad. Sci. Fenn. (Ser. A) 37: 1-20.

Schober, G. 1975. Univalent functions-selected topics. Lecture Note Series. Vol. 478. Berlin: Springer-Verlag.

 

 

 

sebelumnya