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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

© Copyright 1959 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

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