System F-bounded is a second order typed lambda calculus, where the basic features of object-oriented languages can be naturally modelled. F-bounded extends the better known system F≤, in a way that provides an immediate solution for the treatment of the so-called “binary methods”. Although more powerful than F≤ and also quite natural, system F-bounded has only been superficially studied from a...

Suppose that f(z) is a transcendental entire function and that the Fatou set F (f) 6= ∅. Set B1(f) := sup U supz∈U log(|z| + 3) infw∈U log(|w|+ 3) and B2(f) := sup U supz∈U log log(|z|+ 30) infw∈U log(|w| + 3) , where the supremum supU is taken over all components of F (f). If B1(f) < ∞ or B2(f) < ∞, then we say F (f) is strongly uniformly bounded or uniformly bounded respectively. In this arti...

‎Let $X$‎, ‎$Y$ and $Z$ be Banach spaces and $f:Xtimes Y‎ ‎longrightarrow Z$ a bounded bilinear map‎. ‎In this paper we‎ ‎study the relation between Arens regularity of $f$ and the‎ ‎reflexivity of $Y$‎. ‎We also give some conditions under which the‎ ‎Arens regularity of a Banach algebra $A$ implies the Arens‎ ‎regularity of certain Banach right module action of $A$‎ .

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...