We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

Let X be a complex Banach space, a norming set for X , and D ⊂ X a bounded, closed, and convex domain such that its norm closure D is compact in σ(X , ). Let ∅ = C ⊂D lie strictly inside D. We study convergence properties of infinite products of those selfmappings of C which can be extended to holomorphic self-mappings of D. Endowing the space of sequences of such mappings with an appropriate m...

The topology of the weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier Laplace transform of the space of quasianalytic functionals on an open convex subset of R cannot be described by means of weighted supseminorms.

In this paper, L-convex ?*-remotehood system is introduced and some characterizations of both L-convexity remotehood are obtained. Further, ?*-remote mapping presented its properties investigated. Based on this, quasi-uniformity quasiuniformity preserving introduced. It proved that quasi-uniform space Lconvex mutually induced. addition, the category spaces can be embedded into spaces.

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

Let $G=\operatorname {SO}^\circ (n,1) \times \operatorname (n,1)$ and $X=\mathbb {H}^{n}\times \mathbb {H}^{n}$ for $n\ge 2$. For a pair $(\pi _1, \pi _2)$ of non-elementary convex cocompact representations finitely generated group $\Sigma$ into $\operatorname (n,1)$, let $\Gamma =(\pi _1\times _2)(\Sigma )$. Denoting the bottom $L^2$-spectrum negative Laplacian on {\setminus } X$ by $\lambda _...

Let ‖ · ‖ be the euclidean norm on R and γn the (standard) Gaussian measure on R with density (2π)e 2/2. Let θ (≃ 1.3489795) be defined by γ1([−θ/2, θ/2]) = 1/2 and let L be a lattice in R n generated by vectors of norm ≤ θ. Then, for any closed convex set V in R with γn(V ) ≥ 1 2 and for any a ∈ R, (a + L) ∩ V 6= φ. The above statement can be viewed as a “nonsymmetric” version of Minkowski The...