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Mean values for vector valued functions and corresponding functional equations

Ger R., Sablik M.

Commentationes Mathematicae

2013

Vol. 53, No. 2

255--269

Although, in general, a straightforward generalization of the Lagrange mean value theorem for vector valued mappings fails to hold we will look for what can be salvaged in that situation. In particular, we deal with Sanderson's and McLeod's type results of that kind (see [9] and [7], respectively). Moreover, we examine mappings with a prescribed intermediate point in the spirit of the celebrated Aczél's theorem characterizing polynomials of degree at most 2 (cf. [1]).