In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

The aim of this paper is to establish some a priori bounds for solutions of Landesman-Lazer problem. We show the application for the solution structure of the nonlinear diierential equation of the fourth order 1. The general theory Let X be a real Banach space with the norm k k and let D(L) X be the domain of the closed Fredholm operator L : D(L) ! X with index zero. We shall suppose that 0 is ...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

"The purpose of this work is to establish a new generalized form the Krasnoselskii type compression-expansion fixed point theorem for sum an expansive operator and completely continuous one. Applications three non- linear boundary value problems associated second order differential equations coincidence are included illustrate main results."

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

A classical solution of the problem for a quasilinear hyperbolic equation in case two independent variables with given conditions desired function on characteristic lines is obtained. The reduced to system equations completely continuous operator. We constructed unique by method successive approximations and showed necessary sufficient smoothness matching functions.

By computing the completely bounded norm of flip map on Haagerup tensor product [Formula: see text] associated to a pair continuous mappings locally compact Hausdorff spaces text], we establish simple characterization Beck-Chevalley condition for base change operator modules over commutative text]-algebras, and descent theorem fields Hilbert spaces.

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...