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International Journal of Mathematics and Mathematical Sciences
Volume 4, Issue 1, Pages 89-99

A critical investigation of various subclasses of functions whose real part is bounded

Universidade de Brasilia, Departamento de Matematica, Brasilia 70.910, DF, Brazil

Received 22 October 1979

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we investigate various subclasses of univalent analytic functions. We find that many of the subclasses introduced in the recent years are no more new and infact coincide with the class due to Jakubowski. We further study the generalised Jakubowski class of univalent functions and obtain a representational formula and use it in deriving the coefficient relations for this class