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Functional Equations and the Cauchy Mean Value Theorem

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Zoltan M. Balogh, Orif O. Ibrogimov, Boris S. Mityagin

Classical Analysis and ODEs · Submitted 3 Aug 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval.

how it is stated · asserted 0.86 read the record →

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arXiv ID1508.00329 (version 1)
Pith IDXH5SHEUO, Pith's permanent record of this paper and its review
CitationBoris S. Mityagin, Orif O. Ibrogimov, Zoltan M. Balogh. "Functional Equations and the Cauchy Mean Value Theorem." arXiv:1508.00329 (2015). https://pith.science/paper/XH5SHEUO
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,289 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.67 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.17 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. contribution 0.95 0.55 0.25 asserted 0.86
s1 As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel. contribution 0.66 0.90 0.10 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

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