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Roger W Barnard, Charles Kellogg

1980/1

Michigan Mathematical Journal

27

1

81-94

University of Michigan, Department of Mathematics

Roger W. Barnard and Charles Kellogg Page 1 APPLICATIONS OF CONVOLUTION OPERATORS TO) PROBLEMS IN UNIVALENT FUNCTION THEORY Roger W. Barnard and Charles Kellogg In this paper we investigate a wide class of problems. We will exploit the strengths and properties of convolution operators. The strength of these methods lies in their ability to unify a number of diverse results. Of the previously known results obtained in this paper, most of the earlier proofs were tedious examinations of the specific properties of the classes of functions involved. In this paper we are able to obtain and generalize many of these results and obtain a number of new results including a verification of Robinson's 1/2 conjecture in the case of spirallike functions. In general, the proofs using convolution operators are clearer and more concise and point out how the unifying linear structure that is common to so many of the …