Author

# Jong Kyu Kim

Bio: Jong Kyu Kim is an academic researcher from Kyungnam University. The author has contributed to research in topics: Banach space & Fixed point. The author has an hindex of 24, co-authored 165 publications receiving 1748 citations.

##### Papers published on a yearly basis

##### Papers

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01 Mar 2000

TL;DR: Hadic and Pap as discussed by the authors discussed the convergence of Newton's method under unified conditions and the existence and non-existence of approximate fixed points in Generalized Convex Spaces (GCS).

Abstract: 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.

192 citations

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TL;DR: In this paper, the modified block iterative method is used to solve the convex feasibility problems for an infinite family of quasi-asymptotically nonexpansive mappings.

Abstract: 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.

102 citations

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TL;DR: In this article, a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-none-expansive mapping and in the solution set of the equilibrium problem is considered.

Abstract: 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.

92 citations

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TL;DR: An extragradient-type algorithm for solving bilevel pseudomonone variational inequalities using simple projection sequences is presented and the convergence of the iteration sequences generated by the algorithm is obtained.

Abstract: 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.

57 citations

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TL;DR: In this article, a class of set-valued variational inclusions in Banach spaces is introduced and studied by using Michael's selection theorem and Nadler's theorem, and some existence theorems and iterative algorithms for solving this kind of variational inclusion are established and suggested.

52 citations

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01 Jan 2003

2,810 citations

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789 citations

01 Jan 2016

TL;DR: The perturbation analysis of optimization problems is universally compatible with any devices to read and will help you to enjoy a good book with a cup of tea in the afternoon instead of facing with some malicious virus inside their computer.

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461 citations

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TL;DR: In this article, the authors developed a 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.

Abstract: 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.

412 citations

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TL;DR: This letter will study the problem of too little attention paid to the convergence issue of the fixed-point MCC algorithms and give a sufficient condition to guarantee the convergence of a fixed- point MCC algorithm.

Abstract: 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.

264 citations