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1 Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1 1998

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Conic regions k-uniform convexity, II

Kanas S., Wiśniowska A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

65-78

In the previous paper, due to authors, the class of k-uniformly convex functions, (0 < k < oo), has been introduced. Mentioned denoted by kUCV, is a generalization of the class of uniformly convex functions introduced by Goodman, and studied by Ronning, Ma and Minda. This paper is a continuation of investigation of the class k-UCV for that the region of values of 1+ zf'(z)/f'(z), where/ f is an element of k-UCV, is a domain bounded by the conic curves, which kind depends of the parameter k. The estimates of If"(z)I, bounds of coefficients of k-uniformly convex functions, the sharp bounds on |anI, for n= 2,3,4, and the extremal functions which realize equality are given. Some particular examples of functions having the required properties are found.