Let f(z) be a function, meromorphic in \z\ < 1 , whose power series around the origin has integral coefficients. In [5], Salem shows that if there exists a nonzero polynomial p(z) such that p(z)f(z) is in H, or else if there exists a complex number a, such that l/(f(z)—a) is bounded, when |JS| is close to 1, then f(z) is rational. In [2], Chamfy extends Salem's results by showing that if there ...

‎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 $a$‎ .

The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

for all f ∈ Cb(R ) and λ is continuous in the sense that if {fj} ∞ j=1 is a sequence of bounded continuous functions on R which is uniformly bounded and converges uniformly on compact subsets of R to a bounded continuous function f , then {λ(fj)} ∞ j=1 converges to λ(f). If f is any bounded continuous function on R, then there is a sequence {fj} ∞ j=1 of continuous functions on R n such that ea...

We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C smooth (Fréchet smooth or a continuous Gâteaux smooth) function f from X onto Y such that f vanishes outside a bounded set and all the derivatives of f are surjections. In particular we deduce the following result...

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...

We provide necessary and sufficient conditions for a 1-jet (f,G):E→R×X to admit an extension (F,∇F) some F∈C1,ω(X). Here E stands arbitrary subset of Hilbert space X ω is modulus continuity. As corollary, in the particular case X=Rn, we obtain (nonlinear) operator whose norm does not depend on dimension n. Furthermore, construct extensions such way that: (1) (f,G)↦(F,∇F) bounded with respect na...

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

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...