We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.

This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation.

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

King [3] introduced and examined the concepts of almost A-summable sequence, almost conservative matrix and almost regular matrix. In this paper, we introduce and examine the concepts of λ-almost A-summable sequence, λalmost conservative matrix and λ-almost regular matrix. Also we introduce statistically (V, λ)-summable sequence.

L is a continuous function from R× into X and f is a continuous function from R to X . The theory of functional differential equations with infinite delay has been developed by several authors. The fundamental task of that kind of equations is the choice of phase space . Since the history function t→ ut is not continuous in general if u : (−∞,T] → X is continuous (where T > 0). The paper [9] co...

Given two finite sets of integers S ⊆ N \ {0} and D ⊆ N \ {0, 1}, the impartial combinatorial game i-Mark(S,D) is played on a heap of tokens. From a heap of n tokens, each player can move either to a heap of n − s tokens for some s ∈ S, or to a heap of n/d tokens for some d ∈ D if d divides n. Such games can be considered as an integral variant of Mark-type games, introduced by Elwyn Berlekamp ...

Co-author: Lúıs Castro We will present a study of the Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with semi-almost periodic Fourier symbols. The Fredholm property will be described based on certain factorizations of the representatives at infinity of the original symbols, and on the geometrical mean values of the corresponding factors. The Fredholm indices of those oper...