Open AccessON SUBCLASSES OF UNIFORMLY CONVEX FUNCTIONS AND CORRESPONDING CLASS OF STARLIKE FUNCTIONS
Author(s) -
Rakesh Bharati,
R. Parvatham,
A. Swaminathan
Publication year - 1997
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.28.1997.4330
Subject(s) - mathematics , convolution (computer science) , convex function , class (philosophy) , regular polygon , order (exchange) , function (biology) , pure mathematics , combinatorics , geometry , computer science , finance , artificial intelligence , evolutionary biology , artificial neural network , economics , biology , machine learning
We determine a sufficient condition for a function $f(z)$ to be uniformly convex of order et that is also necessary when $f(z)$ has negative coefficients. This enables us to express these classes of functions in terms of convex functions of particular order. Similar results for corresponding classes of starlike functions are also obtained. The convolution condition for the above two classes are discussed.