Conic regions k-uniform convexity, II

• Autorzy: Kanas S. , Wiśniowska A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

convex functions; uniformly convex functions; k-uniformly convex functions; Jacobian elliptic functions

PL

funkcje wypukłe; funkcje jednostajnie wypukłe; funkcje k- jednostajnie wypukłe; funkcje Jacobiana

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 1998
• Tom: z. 22 [170]
• Strony: 65--78
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kanas S.

autor

Wiśniowska A.

• Department of Mathematics, Technical University of Rzeszów