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On mean-value properties for the Dunkl polyharmonic functions

Łysik G.

Opuscula Mathematica

2015

Vol. 35, no. 5

655--664

We derive differential relations between the Dunkl spherical and solid means of continuous functions. Next we use the relations to give inductive proofs of mean-value properties for the Dunkl polyharmonic functions and their converses.

On the bounds for mean-values of solutions to certain third-order non-linear differential equations

Afuwape A. U., Adesina O. A.

Fasciculi Mathematici

2005

Nr 36

5-14

In this paper, the issue of bounds for the mean-values of solutions of some third-order differential equations with non-linear terms is considered. It is shown that these bounds are independent of the solutions for the considered equations.