Here are the titles and abstracts of the seminars which were held in 2010:

Marcin Borkowski**On formal power series**

The aim of the talk is to give an introduction into the theory of formal power series. After the basic definitions and properties we will show some application to combinatorics. Finally, we will show an example of a formal differential equation.

**On the compactness criterion in the space of bounded real-valued continuous functions defined on a non-compact domain**

Marcin Wachowiak**A fixed point theorem for mappings satisfying the interior condition**

(Continuation of the 2010-11-23 and 2010-11-30 Nonlinear seminars).

Marcin Wachowiak**A fixed point theorem for mappings satisfying the interior condition**

(Continuation of the 2010-11-23 Nonlinear Seminar)

Marcin Wachowiak**A fixed point theorem for mappings satisfying the interior condition**

In this talk, we will prove a fixed point theorem for condensing mappings satisfying a new Leray-Schauder type condition proposed by Antonio Jimenez-Melado and Claudio H. Morales, the so-called *interior condition*. We will also show some examples, proving that this condition is in general independent of the classical Leray-Schauder boundary condition. Finally, we will prove that for nonexpansive mappings of Hilbert spaces, the interior condition implies the Leray-Schauder condition.