Loewner's theorem for maps on operator domains

On the Russo-Dye Theorem for positive linear maps

We revisit a classical result, the Russo-Dye Theorem, stating that every positive linear map attains its norm at the identity.

An implicit function theorem for non-smooth maps between Fréchet spaces

We prove an inverse function theorem of Nash-Moser type for maps between Fréchet spaces satisfying tame estimates. In contrast to earlier proofs, we do not use the Newton method, that is, we do not use quadratic convergence to overcome the lack of derivatives. In fact, our theorem holds when the map to be inverted is not C^2

A global bifurcation theorem for critical values of $C^1$ maps in Banach spaces

We present a global bifurcation result for critical values of $C^1$ maps in Banach spaces. The approach is topological based on homotopy equivalence of pairs of topological spaces. For $C^2$ maps, we prove a particular global bifurcation result, based on the notion of spectral flow.

Common fixed point theorems for occasionally weakly compatible maps

In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the literature as those of Aliouche and Popa [15-20]. Also we establish another common fixed point theorem for four owc single and set-valued maps of Gregu% š type which generalizes the results of Djoudi and Nisse, Pathak, Cho, Kang and Madharia and we end our work by giving a third theorem which extends the results given by Elamrani & Mehdaoui and Mbarki.

Common fixed point theorems for pairs of subcompatible maps

In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibilty and reciprocal continuity. With them, we establish several common fixed point theorems which extend corresponding results of Jungck and Rhoades (2006), Djoudi and Nisse (2003) and Mbarki (2002).

An asymptotic variant of the Fubini theorem for maps into CAT(0)-spaces

The classical Fubini theorem asserts that the multiple integral is equal to the repeated one for any integrable function on a product measure space. In this paper, we derive an asymptotic variant of the Fubini theorem for maps into CAT$(0)$-spaces from the $L^1$ and $L^2$-concentration of the maps.

具有收缩轨道的集值映射的不动点定理

Fixed Point Theorems for Set-Valued Maps with Contractive Orbits

研究豪斯多夫空间中限制于轨道时下半连续的集值映射，引入两种收缩轨道概念并建立不动点定理，表明豪斯多夫假设重要，还推广了康托尔交定理，推导了局部凸向量空间及度量前空间中集值映射的不动点定理。

A decomposition theorem for positive maps, and the projection onto a spin factor

It is shown that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal. The result is analyzed in detail for the positive projection onto a spin factor.

Remark on a theorem of H. Hauser on textile maps

We give a counter example to the new theorem that appeared in the survey \cite{H} on Artin approximation. We then provide a correct statement and a proof of it.

Dense Stable Rank and Runge Type Approximation Theorems for $\mathbf{H^\infty}$ Maps

Let $H^\infty(\mathbb D\times\N)$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk $\mathbb D\subset\mathbb C$. We show that the dense stable rank of $H^\infty(\mathbb D\times\N)$ is one and using this fact prove some nonlinear Runge-type approximation theorems for $H^\infty(\mathbb D\times\N)$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for algebra $H^\infty(\mathbb D)$.

随机映射在区间上的接近性、稳定性及中心极限定理

Proximality, stability, and central limit theorem for random maps on an interval

本文研究了区间上随机映射的接近性、稳定性及中心极限定理，证明在满足μ-单射性和某些条件时，这些性质成立。