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Abstrakty
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.
Wydawca
Czasopismo
Rocznik
Tom
Strony
500--509
Opis fizyczny
Bibliogr. 10 poz., rys.
Twórcy
autor
- Department of Mathematics and Computer Science, Barry University, 11300 NE Second Avenue, Miami Shores, FL 33161, United States
Bibliografia
- [1] T. M. Flett, A mean value theorem, Math. Gaz. 42 (1958), 38–39.
- [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-82da6483-3f8d-493f-a5c6-b0ddf95e3124