Iterated quasi-arithmetic mean-type mappings

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

John-type Theorems for Generalized Arithmetic Progressions and Iterated Sumsets

A classical theorem of Fritz John allows one to describe a convex body, up to constants, as an ellipsoid. In this article we establish similar descriptions for generalized (i.e. multidimensional) arithmetic progressions in terms of proper (i.e. collision-free) generalized arithmetic progressions, in both torsion-free and torsion settings. We also obtain a similar characterization of iterated su...

Successive approximations for quasi - firmly type nonexpansive mappings ∗

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...

Automorphisms and quasi-conformal mappings of Heisenberg-type groups

The Lie algebras of trace-zero derivations of Heisenberg-type groups are explicitly characterized, along with the connected component of their groups of measure preserving automorphisms. We establish a general criterion on properties of the stabilizer of a lattice in a simply connected nilpotent Lie group and apply it to the full family of H -type Lie groups. A necessary condition for the exist...

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...