关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Lecture Notes in Economics and Mathematical Systems

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Perturbation Analysis Of Optimization Problems

We develop a versatile general equilibrium framework to determine the spatial distribution of economic activity on (nearly) any surface with (nearly) any geography. Combining the gravity structure of trade with labor mobility, we provide conditions for the existence and uniqueness of a spatial economic equilibrium and derive a simple set of dierential equations which govern the relationship between economic activity and the geography of the surface. We then use the framework to identify the underlying topography of productivities and amenities both in the United States and across the world. We nd that geographic location is an important determinant of the observed spatial distribution of income. Finally, we show how changing the underlying geography would aect the equilibrium distribution of economic activity.

/pdf/trade-and-the-topography-of-the-spatial-economy-3okfb6h45x.pdf

Trade and the Topography of the Spatial Economy

The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.

Fixed Point Theory and Applications

The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-
 -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

/pdf/modified-block-iterative-algorithm-for-solving-convex-jzyz65894f.pdf

Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces

We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property.

/pdf/strong-convergence-theorems-by-hybrid-projection-methods-for-eu4neif0ig.pdf

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.

https://rd.springer.com/content/pdf/10.1007%2Fs10898-012-9870-y.pdf

Jong Kyu Kim

Papers

Fixed Point Theory and Applications

Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

An extragradient algorithm for solving bilevel pseudomonotone variational inequalities

On the existence and iterative approximation problems of solutions for set-valued variational inclusions in Banach spaces