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A Cauchy-type generalization of Flett's theorem

Markov Lubomir

Demonstratio Mathematica

2021

Vol. 54, nr 1

500--509

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.

Generalizations of Lagrange and Cauchy Mean-Value theorems

Matkowski J.

Demonstratio Mathematica

2010

Vol. 43, nr 4

765-774

Some generalizations of the Lagrange Mean-Value Theorem and Cauchy Mean-Value Theorem are proved and the extensions of the corresponding classes of means are presented.