We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...

Branciari [1] obtained a fixed point result for a single mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality. The second author [3] proved two fixed point theorems involving more general contractive conditions. In this paper, we establish a general principle, which makes it possible to prove many fixed point theorems for a pair of maps of integral ty...

Let φ be a one-dimensional surjective cellular automaton map. We prove that if φ is a closing map, then the configurations which are both spatially and temporally periodic are dense. (If φ is not a closing map, then we do not know whether the temporally periodic configurations must be dense.) The results are special cases of results for shifts of finite type, and the proofs use symbolic dynamic...

and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫