Annual Lecture dedicated to the memory of Professor Andrzej Lasota.

In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam–Hyers and in the sense of Ulam–Hyers–Rassias for the integral equation which defines the mild solutions of an abstract Cauchy problem in Banach spaces.

We provide the form of all continuous involutions f of a locally convex linear topological space X such that H∩f(H) = Ø for any basis H of the vector space X over the rationals.

This paper generalises the proof of quadratic reciprocity law in ????_q[T] presented by Chun-Gang Ji and Yan Xue [2] to the case of d-th power residues, where d divides the order of ????^*_q. Using only elementary properties of finite fields and basic number-theoretic tools we show that if P,Q∈????_q[T] are distinct irreducible polynomials then
(P/Q)_d = (-1)^q-1/ddeg(P)deg(Q)(Q/P)_d,
where (P/Q)_d is the d-th power residue symbol.

In the present paper, we establish some results concerning the quasi-Hadamard product for certain subclasses of analytic functions.

By using a particular case of the generalized infimal convolution, we provide an instructive proof for a particular case of a dominated monotone additive extension theorem of Benno Fuchssteiner.

Corrigendum to "A functional equation characterizing homographic functions'' [Annales Mathematicae Silesianae 24 (2010), 61–70].

Report of Meeting: The Eleventh Katowice–Debrecen Winter Seminaron Functional Equations and Inequalities, Wisła-Malinka (Poland), February 2–5, 2011.