• Title, Summary, Keyword: quasi-equilibrium

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A NEW VECTOR QUASI-EQUILIBRIUM-LIKE PROBLEM

  • Lee, Byung-Soo
    • Communications of the Korean Mathematical Society
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    • v.24 no.4
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    • pp.523-528
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    • 2009
  • In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

A STRONG SOLUTION FOR THE WEAK TYPE II GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS

  • Kim, Won-Kyu;Kum, Sang-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.599-610
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    • 2006
  • The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

WEIGHT NASH EQUILIBRIA FOR GENERALIZED MULTIOBJECTIVE GAMES

  • Kim, Won Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.13 no.1
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    • pp.13-20
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    • 2000
  • The purpose of this paper is to give a new existence theorem of a generalized weight Nash equilibrium for generalized multiobjective games by using the quasi-variational inequality due to Yuan.

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A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM

  • Cholamjiak, Prasit;Cholamjiak, Watcharaporn;Suantai, Suthep
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.335-351
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    • 2013
  • In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS OF QUASI-NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITY PROBLEMS

  • Li, Meng;Sun, Qiumei;Zhou, Haiyun
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.813-823
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    • 2013
  • In this paper, a new iterative algorithm involving quasi-nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a quasi-nonexpansive mapping, a solution of an equilibrium problem and the set of solutions of a variational inequality problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (J Math Anal Appl 331:506-515, 2007), P.E.Maing $\acute{e}$ (Computers and Mathematics with Applications, 59: 74-79,2010) and other results in this field.

NEW MAXIMUM THEOREMS WITH STRICT QUASI-CONCAVITY

  • Kim, Won-Kyu;Yoon, Ju-Han
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.565-573
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    • 2001
  • In this paper, we first rove the strict quasi-concavity of maximizing function, and next prove a new maximum theorem using Fan’s generalization of the classical KKM theorem. Also an existence theorem of social equilibrium can be proved when an additional assumption on the constraint correspondence is assumed. Finally, we give illustrative two examples of constrained optimization problems.

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EXTRA-GRADIENT METHODS FOR QUASI-NONEXPANSIVE OPERATORS

  • JEONG, JAE UG
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.467-478
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    • 2016
  • In this paper, we propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of split feasibility, fixed point problems and equilibrium problems of quasi-nonexpansive mappings. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility, fixed point problems and equilibrium problems. An example is given to illustrate the main result of this paper.

A numerical study on the chemically reacting flow at highly altitude (고 고도에서의 화학적 변화를 수반하는 기체 유동에 대한 수치해석적 연구)

  • 이진호;김현우;원성연
    • Journal of the Korea Institute of Military Science and Technology
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    • v.4 no.2
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    • pp.202-214
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    • 2001
  • In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study quasi one-dimensional nozzle flow and axisymmetric sphere-cone($5^{\circ}$) flow for the perfect gas, the equilibrium and the nonequilibrium chemically reacting hypersonic flow. The effective gamma(${ \tilde{\gamma}}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The influences of the various altitude(30km, 50km) at Mach number(15.0, 20.0) were investigated. The equilibrium shock position was located farthest downstream when compared with those of perfect gas in a quasi one-dimensional nozzle. The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock.

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