We study locally compact, geodesically complete, CAT $$(\kappa )$$ spaces ( $$\hbox {GCBA}^\kappa $$ -spaces). prove a Croke-type local volume estimate only depending on the dimension of these spaces. show that doubling condition, with respect to natural measure, implies pure-dimensionality. Then we consider -spaces satisfying uniform packing condition at some fixed scale $$r_0$$ or arbitrarily...

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

Let G be a monoid that acts on topological space X by homeomorphisms such there is point x0∈X with GU=X for each neighbourhood U of x0. A subset said to G-bounded if x0 finite F A⊆FU. We prove metrizable and separable G-space X, the bounded subsets are completely determined any dense subspace. also obtain sufficient conditions locally G-bounded, which apply groups. Thereby, we extend some previ...

amalgam space W (C,L2(R, T 1 1 )) which is locally continuous and globally L2. We show that the sampling or discretization operator R from S to l2(Z, T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S∆ = D∆ S parametrized by the coarseness ∆, and show that the discretization operator is also bounded with a bounded inverse for any ∆ ∈ Zn. This allows us to represent discrete...

In this paper, the focus is on absolute stability and input-to-state stability of the feedback interconnection of an infinite-dimensional linear system Σ and a nonlinearity Φ : dom(Φ) ⊂ Lloc(R+, Y ) → L 2 loc(R+, U), where dom(Φ) denotes the domain of Φ and U and Y (Hilbert spaces) denote the input and output spaces of Σ, respectively (see Figure 1, wherein v is an essentially bounded input sig...

let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...