A Cauchy-type generalization of Flett's theorem

• Autorzy: Markov Lubomir

Identyfikatory

DOI

10.1515/dema-2021-0042

• Języki publikacji: EN

Abstrakty

EN

We prove a Cauchy-type generalization of Flett’s theorem and note its geometric interpretations. Several other mean value theorems extending further the result, which involve both real and complex functions, are also proved.

Słowa kluczowe

EN

Flett’s theorem; Cauchy theorem; Lagrange theorem; mean value theorems; complex Rolle’s theorem; Pawlikowska’s extension of Flett’s theorem

PL

twierdzenie o wartości średniej; twierdzenie Lagrange'a; twierdzenie Cauchy'ego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 500--509
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Markov Lubomir

• Department of Mathematics and Computer Science, Barry University, 11300 NE Second Avenue, Miami Shores, FL 33161, United States

Bibliografia

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• [2] P. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific Publishing, Singapore, 1998.
• [3] R. Davitt, R. Powers, T. Riedel, and P. Sahoo, Flett’s mean value theorem for holomorphic functions, Math. Mag. 72 (1999), 304–307.
• [4] E. Wachnicki, Une variante du théorème de Cauchy de la valeur moyenne, Demonstr. Math. 33 (2000), 737–740.
• [5] M. Ivan, A note on a Cauchy-type mean value theorem, Demonstr. Math. 35 (2002), 493–494.
• [6] D. Trahan, A new type of mean value theorem, Math. Mag. 39 (1966) 264–268.
• [7] O. Hutník and J. Molnárová, On Flett’s mean value theorem, Aequationes Math. 89 (2015), 1133–1165.
• [8] L. Markov, Mean value theorems for analytic functions, Serdica Math. J. 41 (2015), 471–480.
• [9] J.-Cl. Evard and F. Jafari, A complex Rolle’s theorem, Amer. Math. Monthly 99 (1992), 858–861.
• [10] I. Pawlikowska, An extension of a theorem of Flett, Demonstr. Math. 32 (1999), 281–286.