Abstract
Let R denote the family of functions f(z)=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z)>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.
Highlights
Let A denote the class of all functions f of the form ∞f (z) = z + ∑anzn, (1)n=2 which are analytic in the open unit disk U = {z : |z| < 1} and let S denote the subclass of A consisting of univalent functions
Obtain sharp bounds for the coefficient body |Tq(n)|; q = 2, 3; n = 1, 2, 3, where the entries of Tq(n) are the coefficients of functions f of form (1) that are in the family R of functions of bounded boundary rotation
As far as we are concerned, the results presented here are new and noble and the only prior compatible result is published by Thomas and Halim [5] for the classes of starlike and close-to-convex functions
Summary
Let A denote the class of all functions f of the form For f ∈ S we consider the family R of functions of bounded boundary rotation so that Re(f(z)) > 0 in U. Obtain sharp bounds for the coefficient body |Tq(n)|; q = 2, 3; n = 1, 2, 3, where the entries of Tq(n) are the coefficients of functions f of form (1) that are in the family R of functions of bounded boundary rotation.
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