The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani, K. Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Analysis 72 (2010) 1188-1197] from metric spaces to cone metric spaces.
Our aim in this paper is to present a new type of the modular space. This space contains the classical modular space. There are some mappings that do not have contractive condition in the usual modular space but become contraction in this new space.
Coupled fixed point theorems for generalized symmetric Meir--Keeler contractions in ordered metric spaces
本文在半序度量空间中引入广义对称Meir-Keeler压缩，证明了混合单调算子$F:X \times X \rightarrow X$的几个耦合不动点定理.所得结果推广、补充和统一了Samet [B. Samet，\textit{Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces}，非线性分析。\textbf{72}（2010），4508-4517]，Bhaskar和Lakshmikantham [T.G. Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. TMA \textbf{65}（2006）1379-1393]和其他一些非常近期的论文。最后给出了一个例子来说明我们的推广是有效的。
Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces
在半序度量空间中得到了混合$g$ -单调非线性算子$F:X \times X \rightarrow X$的耦合重合和耦合公共不动点定理。我们的结果是最近的重合点定理由于Lakshmikantham和\' Ciri\' c [Lakshmikantham，V.，\' Ciri\' c，L.，\textit{Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces}，非线性分析\textbf{70}（2009），4341-4349]，Bhaskar和Lakshmikantham建立的耦合不动点定理[T.G. Bhaskar，V. Lakshmikantham，\textit{Fixed point theorems in partially ordered metric spaces and applications}，Nonlinear Anal. \textbf{65}（2006）1379-1393]，并且还包括最近文献中的几个相关结果作为特定病例。
We introduce lexicographic cones, a method of assigning an ordered vector space $\Lex(S)$ to a poset $S$, generalising the standard lexicographic cone. These lexicographic cones are then used to prove that the projective tensor cone of two arbitrary cones is a cone, and to find a new characterisation of finite-dimensional vector lattices.
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems …
The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the existence of fixed point can be proved in incomplete metric spaces with non-contraction map on it. We have reported an example in support our result.
We work in an ordered Banach space with closed generating positive cone. We show that a positive compact operator has zero spectral radius or a positive eigenvector with the corresponding eigenvalue equal to the spectral radius.
A version of the classical Klee-Andô Theorem states the following: For every Banach space $X$, ordered by a closed generating cone $C\subseteq X$, there exists some $α>0$ so that, for every $x\in X$, there exist $x^{\pm}\in C$ so that $x=x^{+}-x^{-}$ and $\|x^{+}\|+\|x^{-}\|\leqα\|x\|$. The conclusion of the Klee-Andô Theorem is what is known as a conormality property. We prove stronger and somewhat more general versions of the Klee-Andô Theorem for both conormality and coadditivity (a property that is intimately related to conormality). A corollary to our result shows that the functions $x\ma…
The tensor product of two ordered vector spaces can be ordered in more than one way, just as the tensor product of normed spaces can be normed in multiple ways. Two natural orderings have received considerable attention in the past, namely the ones given by the projective and injective (or biprojective) cones. This paper aims to show that these two cones behave similarly to their normed counterparts, and furthermore extends the study of these two cones from the algebraic tensor product to completed locally convex tensor products. The main results in this paper are the following: (i) drawing pa…
In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.
We define the finest order on inductive limits of ordered cones which makes the linear mappings monotone and gives rise to the definition of inductive limit topologies for cones. Using the polars of neighborhoods, we establish embeddings between direct sums, inductive limits and their duals. These lead us to investigate the weak topologies and the topologies of pointwise convergence in inductive limits.
Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces.
Comparison of spectral radii and Collatz-Wielandt numbers for homogeneous maps, and other applications of the monotone companion norm on ordered normed vector spaces
众所周知，具有法锥$X_+$的有序赋范向量空间$X$具有与原始范数等价的保序范数。\begin{equation} \sharp x \sharp = \max \{ d(x, X_+), d(x, - X_+)\}, \qquad x \in X. \end{equation}给出了这样一个等价的保序范数。本文讨论了这个范数和半范数$ψ(x) = d(x,-X_+)$的性质，与锥是否正规无关。我们使用$ψ$推导抽象积分方程解的比较原理，推导非线性正映射点耗散性的条件，比较有界齐次映射的Collatz-Wielandt数、界和序谱半径，并给出局部上Collatz-Wielandt半径具有下正特征向量的条件.
With the notion of mode-$j$ Birkhoff contraction ratio, we prove a multilinear version of the Birkhoff-Hopf and the Perron-Fronenius theorems, which provide conditions on the existence and uniqueness of a solution to a large family of systems of nonlinear equations of the type $f_i(x_1,\dots,x_ν)= λ_i x_i$, being $x_i$ and element of a cone $C_i$ in a Banach space $V_i$. We then consider a family of nonlinear integral operators $f_i$ with positive kernel, acting on product of spaces of continuous real valued functions. In this setting we provide an explicit formula for the mode-$j$ contraction…
Cones and gauges in complex spaces : Spectral gaps and complex Perron-Frobenius theory
我们引入复锥和相关的射影规范，推广了一个真正的伯克霍夫锥和希尔伯特度量复向量空间。在复巴拿赫空间中，我们推出了一系列谱间隙定理。证明了一个控制复锥压缩定理，并利用它将经典的Perron-Frobenius定理推广到复矩阵，将Jentzsch定理推广到复积分算子，将Krein-Rutman定理推广到紧和准紧的复算子，将Ruelle-Perron-Frobenius定理推广到动力系统的复转移算子.在一个复杂的n乘n矩阵A的最简单的情况下，我们有下面的陈述：假设0 < c < +无穷大使得|Im A_{ij} \bar{A}_{mn}| < c < Re A_{ij} \bar{A}_{mn}对于所有指数。那么A有一个“光谱间隙”。
Results of a previous paper [Commun. Contemp. Math., 09 (2007) 217-251] on the existence of solutions to a nonlinear evolution equation in an abstract Lebesgue space, arising from kinetic theory, are re-obtained in the more general setting of a real ordered Banach space, with additive norm on the positive cone, which is not necessarily a (Banach) lattice. In addition, an easily correctable technical error in the aforementioned paper is pointed out, and repaired.
