Invariant property for discontinuous mean-type mappings

Invariant Graphs of Functions for the Mean-type Mappings

Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, . . . ,Mp : I → I the continuous means. We consider the problem of invariance of the graphs of functions φ : Jp−1 → I with respect to the mean-type mapping M = (M1, . . . ,Mp) . Applying a result on the existence and uniqueness of an M-invariant mean [7], we prove that if the graph of a continuous function φ : Jp−1...

Invariant Mean Value Property and Harmonic Functions

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.

Iterations of the Mean-type Mappings and Uniqueness of Invariant Means

It is known, that under some natural conditions, the iterates of any continuous mean-type mapping converge to a continuous invariant mean-type mapping, and, moreover, the invariant continuous mean-type mapping is unique. In this paper we show that the assumption of the continuity in the ”moreover” part of this result is superfluous. We also show that every increasing and homogeneous mean is con...

Translation invariant mappings on KPC-hypergroups

In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.

An invariant for continuous mappings