Existence and comparison results for fixed points of multifunctions with applications to normal-form games

In this paper we apply generalized iteration methods to prove comparison results which show how fixed points of a multifunction can be bounded by least and greatest fixed points of single-valued functions. As an application we prove existence and comparison results for fixed points of multifunctions. These results are applied to normal-form games, by proving existence and comparison results for pure and mixed Nash equilibria and their utilities.     

A note on fixed point sets in CAT(0) spaces

We show that the fixed point set of a quasi-nonexpansive selfmap of a nonempty convex subset of a CAT(0) space is always closed, convex and contractible. Moreover, we give a construction of a continuous selfmap of a CAT(0) space whose fixed point set is prescribed.     

Contractive maps on normed linear spaces and their applications to nonlinear matrix equations

In this paper we will give necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space. These conditions are already well known for maps on intervals in R. Using the conditions and Banach’s fixed point theorem we can prove a fixed point theorem for operators on a normed linear space. The fixed point theorem will be applied to the matrix equation X = I_n + A^∗f(X)A, where f is a map on the set of positive definite matrices induced by a real valued map on (0, ∞). This will give conditions on A and f under which the equation has a unique solution in a certain set. We will consider two examples of f in detail. In one example the application of the fixed point theorem is the first step in proving that the equation has a unique positive definite solution under the conditions on A.     

Systems of differential inclusions with maximal monotone terms

In this paper, we establish the existence of solutions to systems of second order differential inclusions with maximal monotone terms. Our proofs rely on the theory of maximal monotone operators and the Schauder degree theory. A notion of solution-tube to these problems is introduced. This notion generalizes the notion of upper and lower solutions of second order differential equations.     

Solvability of a neutral differential equation with deviated argument

The paper contains theorem on the existence and asymptotic characterization of solutions of a differential equation of neutral type with deviated argument. The mentioned differential equation admits both delayed and advanced arguments. In our considerations we use the technique linking measures of noncompactness with the classical Schauder fixed point principle.     

Bounded continuous nonoscillatory solutions of second-order nonlinear difference equations with continuous variable

In this paper, by using the fixed point theory, under quite general condition on the nonlinear term, we obtain an existence result concerning bounded continuous nonoscillatory solutions of a second-order nonlinear difference equation with continuous variable.     

Weak topology and Browder-Kirk's theorem on hyperspace

Let K be a weakly compact, convex subset of a Banach space X with normal structure. Browder-Kirk's theorem states that every non-expansive mapping T which maps K into K has a fixed point in K. Suppose now that WCC(X) is the collection of all non-empty weakly compact convex subsets of X. We shall define a certain weak topology Tw on WCC(X) and have the above-mentioned result extended to the hyperspace (WCC(X);Tw).     

双锥不动点定理及其在非线性边值问题中的应用

本文研究了具可变号非线性项的非线性边值问题的正解存在性,推广了 Krasnoselskii 不动点定理,得到了新的锥上不动点定理,并应用这些定理给出这类边值问题正解的存在性．     

Off-diagonal long-range order and the Meissner effect

We provide a general, model-independent, derivation of the Meissner effect, on the basis of assumptions of off-diagonal long-range order (ODLRO) and gauge covariance of the second kind. This is an exact result that is independent of the microscopic mechanism responsible for the ordering, and so is applicable both to high- and low-T _c superconductors.     

Stripe noise removal for infrared image by minimizing difference between columns

This paper introduces a novel approach to eliminate stripe noise in infrared images. The differences between bias voltages in column readout circuit of uncooled infrared sensors result in strong stripe noise which changes slowly in time. The problem can be solved by estimating the bias of each column of infrared images and correcting infrared images with the estimated biases. The bias estimation is translated into an energy optimization problem in the paper. The optimization aims to minimize difference between neighboring columns of images. Our approach can be processed on a single image, or in a recursive way in order to significantly reduce the computation in one frame time. Our approach is compared to the state-of-the-art the stripe noise removal method using realistic infrared images, and the experimental results show the effectiveness and efficiencies of our proposed approach.