We construct a σ-ideal of subsets of the Cantor space which is productive but does not have the Weak Fubini Property. In the construction we use a combinatorial lemma which is of its own interest.

An Ohm–Rush algebra $$R \rightarrow S$$ is called McCoy if for any zero-divisor f in S, its content c(f) has nonzero annihilator R, because proved this when $$S=R[x]$$ . We answer a question of Nasehpour by giving class examples faithfully flat algebras with the property that are not weak algebras. However, we show iff $$R/I S/I all radical (resp. prime) ideals I R. When R Noetherian (or more g...

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

Type hierarchies which arise in applications are often described incompletely; this missing information may be handled in a variety of ways. In this work, such incomplete hierarchies are viewed as open specifications; that is, descriptions which are sets of constraints. The actual hierarchy is then any structure satisfying these constraints. For such specifications, two forms of characterizatio...