Let be a real Banach space, let be a closed convex subset of , and let , from into , be a pseudo-contractive mapping (i.e. for all and 1)$">. Suppose the space has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of enjoys the Fixed Point Property for nonexpansive self-mappings. Then the path , , defined by the equation is continuous and strongly converges to a fixed point of as , provided that satisfies the weakly inward condition.
Under suitable assumptions on , we prove that generates a positive -semigroup on and, hence, many previous (linear or nonlinear) results are extended substantially.
If and are linear operators acting between Banach spaces, we show that compactness of relative to does not in general imply that has -bound zero. We do, however, give conditions under which the above implication is valid.
On bounded domains we consider the anisotropic problems in with 1$"> and on and in with and on . Moreover, we generalize these boundary value problems to space-dimensions 2$">. Under geometric conditions on and monotonicity assumption on we prove existence and uniqueness of positive solutions. 相似文献
For a knot in the -sphere, by using the linking form on the first homology group of the double branched cover of the -sphere, we investigate some numerical invariants, -genus , nonorientable -genus and -dimensional clasp number , defined from the four-dimensional viewpoint. T. Shibuya gave an inequality , and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.
Let be the Iwasawa decomposition of a complex connected semi-simple Lie group . Let be a parabolic subgroup containing , and let be its commutator subgroup. In this paper, we characterize the -invariant Kähler structures on , and study the holomorphic sections of their corresponding pre-quantum line bundles.
We introduce the notion of a Banach space containing an asymptotically isometric copy of . A well known result of Bessaga and Peczynski states a Banach space contains a complemented isomorphic copy of if and only if contains an isomorphic copy of if and only if contains an isomorphic copy of . We prove an asymptotically isometric analogue of this result.
Suppose is a block of a group algebra with cyclic defect group. We calculate the Hochschild cohomology ring of , giving a complete set of generators and relations. We then show that if is the principal block, the canonical map from to the Hochschild cohomology ring of induces an isomorphism modulo radicals. 相似文献
For a bounded invertible operator on a complex Banach space let be the set of operators in for which Suppose that and is in A bound is given on in terms of the spectral radius of the commutator. Replacing the condition in by the weaker condition as for every 0$">, an extension of the Deddens-Stampfli-Williams results on the commutant of is given.
Let be a vector lattice of real functions on a set with , and let be a linear positive functional on . Conditions are given which imply the representation , , for some bounded charge . As an application, for any bounded charge on a field , the dual of is shown to be isometrically isomorphic to a suitable space of bounded charges on . In addition, it is proved that, under one more assumption on , is the integral with respect to a -additive bounded charge.
In this note it is shown that if is an ``algebraically hyponormal" operator, i.e., is hyponormal for some nonconstant complex polynomial , then for every , Weyl's theorem holds for , where denotes the set of analytic functions on an open neighborhood of .