The homotopies of admissible multivalued mappings

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.     

Coincidence theorem for admissible set-valued mappings and its applications in FC-spaces

A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.     

Connection digraphs and second-order line digraphs

The primary result of this paper gives a set of necessary and sufficient conditions for a digraph to be second-order line digraph of some digraph. A directed analogue of the concept of an intersection graph, defined for collections of ordered pairs of sets and called the connection digraph, is used to achieve this result.     

On super-edge-connected digraphs and bipartite digraphs

A maximally edge-connected digraph is called super-λ if every minimum edge disconnecting set is trivial, i.e., it consists of the edges adjacent to or from a given vertex. In this paper sufficient conditions for a digraph to be super-λ are presented in terms of parameters such as diameter and minimum degree. Similar results are also given for bipartite digraphs. As a corollary, some characterizations of super-λ graphs and bipartite graphs are obtained. © 1929 John Wiley & Sons, Inc.     

Relational Galois connections between transitive fuzzy digraphs

Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering.     

Some relationships between induced mappings

We prove some relationships between f, Cn(f), HSn(f) and f², when f, Cn(f), HSn(f) or f² belong to the following mapping classes: monotone, OM, confluent, semi-confluent, weakly confluent, pseudo-confluent, quasi-monotone, weakly monotone or joining.     

Inclusion mappings between lp spaces

It is shown that the inclusion mapping from $\text{l}{}^{\mathrm{p}}\text{into}\text{l}{}^{\mathrm{q}}\text{is}\text{(}\text{2pq}\text{(pq ? 2p + 2q)}\text{, 1)}$-absolutely summing if 1 ? p ? q ? 2 and (p, 1)-absolutely summing if 1 ? p ? 2 ? q ? ∞ or 2 ? p ? q ? ∞. As a corollary, it follows that a (p, 1)-absolutely summing operator, p > 1, need not have the Dunford-Pettis property; this observation answering a question raised by Pelczynski.     

Integral mappings between Banach spaces

We consider the classes of “Grothendieck-integral” (G-integral) and “Pietsch-integral” (P-integral) linear and multilinear operators (see definitions below), and we prove that a multilinear operator between Banach spaces is G-integral (resp. P-integral) if and only if its linearization is G-integral (resp. P-integral) on the injective tensor product of the spaces, together with some related results concerning certain canonically associated linear operators. As an application we give a new proof of a result on the Radon-Nikodym property of the dual of the injective tensor product of Banach spaces. Moreover, we give a simple proof of a characterization of the G-integral operators on C(K,X) spaces and we also give a partial characterization of P-integral operators on C(K,X) spaces.     

Infinite highly arc transitive digraphs and universal covering digraphs

A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraphDL() is constructed and is shown to be a covering digraph for every digraph in a certain classD() of connected digraphs. Moreover, if is locally finite, thenDL() is a universal covering digraph forD(). Further constructions of infinite highly arc transitive digraphs are given.The second author wishes to acknowledge the hospitality of the Mathematical Institute of the University of Oxford, and the University of Auckland, during the period when the research for this paper was doneResearch supported by the Australian Research Council     

Quasiconformal and harmonic mappings between Jordan domains

Let Ω and Ω₁ be Jordan domains, let μ ∈ (0, 1], and let be a harmonic homeomorphism. The object of the paper is to prove the following results: (a) If f is q.c. and ∂Ω, ∂Ω₁ ∈ C ^1,μ , then f is Lipschitz; (b) if f is q.c., ∂Ω, ∂Ω₁ ∈ C ^1,μ and Ω₁ is convex, then f is bi-Lipschitz; and (c) if Ω is the unit disk, Ω₁ is convex, and ∂Ω₁ ∈ C ^1,μ , then f is quasiconformal if and only if its boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in L ^∞. These extend the results of Pavlović (Ann. Acad. Sci. Fenn. 27:365–372, 2002).      

Proper holomorphic mappings between generalized pseudoellipsoids

Summary We characterize the existence of proper holomorphic mappings between pseudoellipsoids of the form . If f:()() is any such mapping, the existence of a subgroup of Aut (()) such that is shown equivalent to a condition on the branch locus of f.