SOME RESULTS ASSOCIATED WITH CONVOLUTION INVOLVING CERTAIN CLASSES OF UNIFORMLY STARLIKE AND CONVEX FUNCTIONS WITH NEGATIVE COEFFICIENTS
OYEKAN, EZEKIEL ABIODUN *
Department of Mathematical Sciences, Ondo State University of Science and Technology, P.M.B 353, Okitipupa, Ondo State, Nigeria
*Author to whom correspondence should be addressed.
Making use of the convolution property of two analytic functions, we define new classes of uniformly starlike and convex functions with negative coefficients and obtain characterization properties which include coefficient estimates, growth and distortion, convex linear combinations, extreme points and closure theorems. Further results on integral transforms are also discussed.
Keywords: Analytic functions, extreme point, integral transform, convolution, negative coefficients, distortion theorems