Abstract.We investigate starlike functions f(z) = z + Yfk=2akzk wim the property that zf'(z)/'f(z) lies inside a certain parabola. These functions are closely related to a class of functions called uniformly convex and recently introduced by Goodman. We give some particular examples of functions having the required properties, and we give upper bounds on the coefficients and the modulus \f(z)\ of the functions in the class.
Abstract. For α ≥ 0 let Fα denote the class of functions defined for |z| < 1 by integrating 1/(1 − xz) α if α > 0, and log(1/(1 − xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf (z)/f (z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to F 0 . In general, it is only known that bounded starlike functions belong to Fα for α > 0.
This paper is based on an on-going project for modernizing the basic education in mathematics for engineers at the Norwegian University of Science and Technology. One of the components in the project is using a computer-aided assessment system (Maple T.A.) for handling students' weekly hand-ins. Successful completion of a certain number of problem sets in Maple T.A. is required for being admitted to the final examination. This also gives partial credit towards the final grade. In this paper, I will look at possible influence Maple T.A. may have on the ways students engage with the mathematical problems.
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