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Further Results of Mean-Value Type in \({\mathbb {C}}\) and \({\mathbb {R}}\)

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Advanced Computing in Industrial Mathematics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 681))

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Abstract

We prove an extension of Pompeiu’s Mean Value Theorem to holomorphic functions in the spirit of the Evard-Jafari Theorem, a (new?) mean value theorem in \(\mathbb R,\) and an extension of the latter in \({\mathbb {C}}.\)

This paper was presented at the international conference “BGSIAM’15” (10th Annual Meeting of the Bulgarian Section of SIAM), 21–22 December 2015, Sofia, Bulgaria.

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References

  1. Davitt, R., Powers, R., Riedel, T., Sahoo, P.: Flett’s mean value theorem for holomorphic functions. Math. Mag. 72, 304–307 (1999)

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  3. Flett, T.M.: A mean value theorem. Math. Gazette 42, 38–39 (1958)

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  4. Markov, L.: Mean value theorems for analytic functions. Serdica Math. J. 41, 471–480 (2015)

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  5. Pompeiu, D.: Sur une proposition analogue au théorème des accroissements finis. Mathematica (Cluj) 22, 143–146 (1946)

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  6. Sahoo, P., Riedel, T.: Mean Value Theorems and Functional Equations. World Scientific Publishing Singapore (1998)

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Correspondence to Lubomir Markov .

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Markov, L. (2017). Further Results of Mean-Value Type in \({\mathbb {C}}\) and \({\mathbb {R}}\) . In: Georgiev, K., Todorov, M., Georgiev, I. (eds) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol 681. Springer, Cham. https://doi.org/10.1007/978-3-319-49544-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-49544-6_11

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