On summability of nonlinear mappings: a new approach
Daniel Pellegrino, Joedson Santos
备注：
This new presentation of the manuscript (quite modified and reduced) is the version accepted for publication in Math. Z. Part of the old version (which does not appear in this new version) will appear in a forthcoming paper
发表信息：
Mathematische Zeitschrift, v. 270, p. 189-196, 2012
The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_{1},...,a_{n})\in$ $X_{1}\times...\times X_{n}$. As a consequence of our approach a notion of weighted summability arises naturally, which may be an interesting topic for further investigation.
Best proximity point results for almost contraction and application to nonlinear differential equation
Brinde [Approximating不动点of weak contractions using the Picard itration，Nonlinear Anal. Forum 9（2004），43-53]引入了几乎压缩映射，并证明了几乎压缩映射的Banach压缩原理。引入了集值几乎$Θ$ -压缩映射的概念，并给出了这类映射的最佳邻近点结果。作为应用，得到了弱单值$Θ$ -压缩映射的最佳邻近点和不动点的结果。一个例子来支持本文提出的结果。最后给出了一个非线性微分方程的应用。
Fixed point properties for semigroups of nonlinear mappings on unbounded sets
W. Ray断言，如果$C$是Hilbert空间的无界凸集，则存在一个没有不动点的非扩张映射$T$：$C\to C$。本文讨论了作用在Hilbert空间的闭凸子集$C$上的非扩张映射的拓扑半群$S$的一些公共不动点性质，并假定存在一个轨道有界的点$c\in C$，以及假定$C_b(S)$的某个子空间具有左不变平均.左不变平均（或称顺从性）是半群和群的调和分析中的一个重要概念，由von Neumann在1929年\cite{Neu}中引入，并由Day在1957年\cite{Day}中形式化。在我们的研究中，我们使用了最近由S。Atsushiba和W.高桥
Coupled fixed point theorems for $ϕ$-contractive mixed monotone mappings in partially ordered metric spaces
本文推广了[T.G.]中关于混合单调算子$F:X \times X \rightarrow X$的耦合不动点定理。Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. \textbf{65}（2006）1379-1393]和[N. V. Luong和N.X. Thuan，\textit{Coupled fixed points in partially ordered metric spaces and application}，Nonlinear Anal. \textbf{74}（2011）983-992]，通过削弱所涉及的收缩条件。为了说明推广的有效性，还给出了一个例子以及对非线性弗雷德霍姆积分方程的应用.
Some remarks on smooth mappings of Hilbert and Banach spaces and their local convexity property
University of Agriculture in Krakow（克拉科夫农业大学）；Institute of Mathematics of NAS of Ukraine（乌克兰国家科学院数学研究所）；Lviv Polytechnic National University（利沃夫国立理工大学）；Comenius University in Bratislava（布拉迪斯拉发康斯坦丁尼查尔大学）
Nonlinear and orbital directional regularities for set-valued mappings and applications to fixed points
Faculty of Mathematics, “Alexandru Ioan Cuza” University（亚历山德鲁·约安·库扎大学数学系）；“Octav Mayer” Institute of Mathematics, Iaşi Branch of Romanian Academy（罗马尼亚科学院雅西分院奥克塔夫·梅耶尔数学研究所）；Department of Mathematics and Statistics, Quy Nhon University（归仁大学数学与统计系）；XLIM UMR-CNRS 7252, Université de Limoges（利摩日大学XLIM UMR-CNRS 7252）
