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S. Park's Contribution to the Development of Fixed Point Theory and KKM Theory

  1. Research

    Applications of some basic theorems in the KKM theory

    In this review, we introduce a new KKM-type theorem for intersectionally closed-valued KKM map on abstract convex spaces and its direct consequences such as a Fan-Browder-type fixed point theorem and maximal e...

    Sehie Park

    Fixed Point Theory and Applications 2011 2011:98

    Published on: 7 December 2011

  2. Research

    Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization

    In this paper, we consider a class of nonsmooth multiobjective programming problems. Necessary and sufficient optimality conditions are obtained under higher order strongly convexity for Lipschitz functions. W...

    Kwan Deok Bae and Do Sang Kim

    Fixed Point Theory and Applications 2011 2011:42

    Published on: 25 August 2011

    The Erratum to this article has been published in Fixed Point Theory and Applications 2012 2012:28

  3. Research

    Common fixed points of R-weakly commuting maps in generalized metric spaces

    In this paper, using the setting of a generalized metric space, a unique common fixed point of four R-weakly commuting maps satisfying a generalized contractive condition is obtained. We also present example in s...

    Mujahid Abbas, Safeer Hussain Khan and Talat Nazir

    Fixed Point Theory and Applications 2011 2011:41

    Published on: 22 August 2011

  4. Research Article

    An Implicit Iteration Method for Variational Inequalities over the Set of Common Fixed Points for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

    We introduce a new implicit iteration method for finding a solution for a variational inequality involving Lipschitz continuous and strongly monotone mapping over the set of common fixed points for a finite fa...

    Nguyen Buong and NguyenThi Quynh Anh

    Fixed Point Theory and Applications 2011 2011:276859

    Published on: 15 March 2011

  5. Research Article

    Approximation of Common Solutions to System of Mixed Equilibrium Problems, Variational Inequality Problem, and Strict Pseudo-Contractive Mappings

    We introduce an iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions mapping, the set of common solutions of a system of two mixed equilibrium problems and t...

    Poom Kumam and Chaichana Jaiboon

    Fixed Point Theory and Applications 2011 2011:347204

    Published on: 14 March 2011

  6. Research Article

    Strong Convergence Theorems for an Infinite Family of Equilibrium Problems and Fixed Point Problems for an Infinite Family of Asymptotically Strict Pseudocontractions

    We prove a strong convergence theorem for an infinite family of asymptotically strict pseudo-contractions and an infinite family of equilibrium problems in a Hilbert space. Our proof is simple and different fr...

    Shenghua Wang, ShinMin Kang and YoungChel Kwun

    Fixed Point Theory and Applications 2011 2011:859032

    Published on: 23 February 2011

  7. Research Article

    Finding Common Solutions of a Variational Inequality, a General System of Variational Inequalities, and a Fixed-Point Problem via a Hybrid Extragradient Method

    We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-po...

    Lu-Chuan Ceng, Sy-Ming Guu and Jen-Chih Yao

    Fixed Point Theory and Applications 2010 2011:626159

    Published on: 29 December 2010