Home > Iowa Academy of Science > Journals & Newsletters > Proceedings of the Iowa Academy of Science > Volume 66 (1959) > Annual Issue
Document Type
Research
Abstract
The generalized mean M(x,y) is defined to be Ψ-1 [pΨ (x) + aΨ (y)] where p, a>0, p + a = 1 and Ψ (x) is monotone and continuous.
This mean is applied to the second difference. Δ2(f: x, h) = f(x+h) + (f-h)-2f(x) to form a generalized second difference Δ2Ψ (f: x, h) = MΨ [f(x+h), f(x-h)] - f(x)..
A study is made of functions whose generalized second differences satisfy certain conditions. Maxima of classes of generalized quasi-smooth functions are examined. It is the purpose of this note to apply the generalized mean to the study of second differences. A generalized second difference will be defined and certain properties of the second difference will be examined under this generalization.
Publication Date
1959
Journal Title
Proceedings of the Iowa Academy of Science
Volume
66
Issue
1
First Page
357
Last Page
361
Copyright
©1959 Iowa Academy of Science, Inc.
Language
en
File Format
application/pdf
Recommended Citation
Nolte, Sidney D.
(1959)
"An Application of Generalized Means,"
Proceedings of the Iowa Academy of Science, 66(1), 357-361.
Available at:
https://scholarworks.uni.edu/pias/vol66/iss1/48