Real Analysis Exchange

Approximately Continuous Functions Have Approximate Extrema, a New Proof

Chris Freiling, Paul D. Humke, and Richard J. O'Malley

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Abstract

In 1975, Richard O’Malley proved that every approximately continuous function has approximate extrema, and this result provides an immediate solution to SB 157. The purpose of this paper is to provide an additional proof of O’Malley's result.

Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 409-414.

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839342

Mathematical Reviews number (MathSciNet)
MR3597330

Zentralblatt MATH identifier
1384.26022

Subjects
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 26A48: Monotonic functions, generalizations

Keywords
approximate maximum approximate continuity

Citation

Freiling, Chris; Humke, Paul D.; O'Malley, Richard J. Approximately Continuous Functions Have Approximate Extrema, a New Proof. Real Anal. Exchange 41 (2016), no. 2, 409--414. https://projecteuclid.org/euclid.rae/1490839342


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