Normality and fixed-points of meromorphic functions

LetF be families of meromorphic functions in a domainD, and letR be a rational function whose degree is at least 3. If, for anyf∈ F, the composite functionR(f) has no fixed-point inD, thenF is normal inD. The number 3 is best possible. A new and much simplified proof of a result of Pang and Zalcman concerning normality and, shared values is also given.     

Uniqueness theorems for meromorphic functions concerning fixed-points

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials that share fixed-points. Moreover, we greatly improve a former result.     

On fixed-points and singular values of transcendental meromorphic functions

In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for ...     

Common fixed-points for Banach operator pairs in best approximation

The notion of Banach operator pairs is introduced, as a new class of noncommuting maps. Some common fixed-point theorems for Banach operator pairs and the existence of the common fixed-points of best approximation are presented. These results are proved without the assumption of linearity or affinity for either f or g, which shows that the concept about Banach operator pairs is potentially useful in the study of common fixed-points.     

Permanent analogues of determinantal identities related to permutation fixed-points

We present permanent analogues of a determinantal identity due to A. Cayley and a formula computing the determinant of so-called zero-axial matrices, for both the generic commuting and noncommuting cases. The Cayley theorem and its permanental versions are derived using combinatorial interpretation of a classical binomial identity The Theorems concerning zero-axial matrices are gotten by the principle of inclusion-exclusion.     

Local Completeness and Drop Theorem

By using the concept of local completeness, we extend Danes' Drop Theorem to locally convex spaces.     

Some fixed-points theorems for multi-valued mappings in topological vector spaces

Sunto Si danno dei teoremi di punto fisso der trasformazioni multivoche non compatte, definite in un sottoinsieme convesso e chiuso di uno spazio lineare topologico, localmente convesso e di Hausdorff. Tali teoremi estendono alcuni noti risultati dovuti a Darbo, Sadovskij, Daneš ed altri.

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Work performed under the auspices of the National Research Council (C.N.R.).

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Entrata in Redazione il 18 maggio 1971.     

Banach压缩映象原理与空间完备性

本文进一步揭示了Ｂａｎａｃｈ压缩映象原理与完备性的关系，指出：一般地，Ｂａｎａｃｈ压缩映象原理等价于道路完备性，在一定条件下才等价于完备性，进一步给出了这一等价性成立的充要条件     

Completeness, Sections and Selections

In this paper, we develop a general approach to set-valued semi-continuous selections which is based on order-like arguments rather than on classical approximations. The approach works nice in a number of situations demonstrating the genesis of such selection properties of set-valued mappings. In particular, it allows to generalize several known results, also to get some new results about sections of set-valued mappings.      

Weakly Cauchy Filters and Quasi-Uniform Completeness

It is well-known that the notion of a Smyth complete quasi-uniform space provides an appropriate notion of completeness to study many interesting quasi-metric spaces which appear in theoretical computer science. We observe that several of these spaces actually possess a stronger form of completeness based on the use of weakly Cauchy filters in the sense of H. H. Corson and we develop a theory of completion and completeness for this kind of filters. In parallel, we also study a more general notion of completeness based on the use of certain stable filters. Thus our results extend and generalize important theorems of Á. Császár, J. R. Isbell and N. R. Howes on uniform completeness.     

Lawvere Completeness in Topology

It is known since 1973 that Lawvere’s notion of Cauchy-complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper, we introduce the corresponding notion of Lawvere completeness for (\mathbbT,V)(\mathbb{T},\mathsf{V})-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones it means weak sobriety while for the latter it means Cauchy completeness. Further, we show that V\mathsf{V} has a canonical (\mathbbT,V)(\mathbb{T},\mathsf{V})-category structure which plays a key role: it is Lawvere-complete under reasonable conditions on the setting; this structure permits us to define a Yoneda embedding in the realm of (\mathbbT,V)(\mathbb{T},\mathsf{V})-categories.     

Exact finite-difference schemes for first order differential equations having three distinct fixed-points

We construct nonstandard finite-difference (NSFD) schemes that provide exact numerical methods for a first-order differential equation having three distinct fixed-points. An explicit, but also nonexact, NSFD scheme is also constructed. It has the feature of preserving the critical properties of the original differential equation such as the positivity of the solutions and the stability behavior of the three fixed-points.     

Bergman 穷竭, 完备与稳定性

Bergman核是国内外研究多复变函数论的一个传统课题,本文主要介绍利用超定的非齐次Cuauchy-Riemann方程组的现代Hilbert空间理论研究Bergman核的穷竭性,稳定性与Bergman度量的完备性所取得的最新进展。     

Positivity and Completeness of Invariant Metrics

We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains in \(\mathbb {C}^n\). As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains.     

Completeness for intersection classes

An intersection representation of a graph is a function gf mapping vertices to sets such that for any u ≠ v, u is adjacent to v iff gf(u) ∩ gf(v) ≠ . The intersection class defined by a set of sets ∑ is the set of all graphs having an intersection representation using sets from ∑. Interval graphs and chordal graphs are well-studied examples of intersection classes.

This paper introduces the notion of completeness for intersection classes. That is, determining precisely what restrictions can be made on the allowable sets without losing the power to represent any graph in the intersection class. The solution to this problem is presented for the chordal graphs.     

Sequential Completeness of LF-Spaces

Any LF-space is sequentially complete iff it is regular.