• Title/Summary/Keyword: equilibrium problems

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A PARALLEL HYBRID METHOD FOR EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS IN HILBERT SPACE

  • Hieu, Dang Van
    • Journal of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.373-388
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    • 2015
  • In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

NUMERICAL SOLUTION OF EQUILIBRIUM EQUATIONS

  • Jang, Ho-Jong
    • Communications of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.133-142
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    • 2000
  • We consider some numerical solution methods for equilibrium equations Af + E$^{T}$ λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible fluid flow. We also suggests some iterative methods based upon substructuring scheme..

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A GENERAL ITERATIVE METHOD BASED ON THE HYBRID STEEPEST DESCENT SCHEME FOR VARIATIONAL INCLUSIONS, EQUILIBRIUM PROBLEMS

  • Tian, Ming;Lan, Yun Di
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.603-619
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    • 2011
  • To the best of our knowledge, it would probably be the first time in the literature that we clarify the relationship between Yamada's method and viscosity iteration correctly. We design iterative methods based on the hybrid steepest descent algorithms for solving variational inclusions, equilibrium problems. Our results unify, extend and improve the corresponding results given by many others.

MODIFIED SUBGRADIENT EXTRAGRADIENT ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

  • Dang, Van Hieu
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1503-1521
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    • 2018
  • The paper introduces a modified subgradient extragradient method for solving equilibrium problems involving pseudomonotone and Lipschitz-type bifunctions in Hilbert spaces. Theorem of weak convergence is established under suitable conditions. Several experiments are implemented to illustrate the numerical behavior of the new algorithm and compare it with a well known extragradient method.

STRONG CONVERGENCE THEOREM OF COMMON ELEMENTS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

  • Zhang, Lijuan;Hou, Zhibin
    • East Asian mathematical journal
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    • v.26 no.5
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    • pp.599-605
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    • 2010
  • In this paper, we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of an asymptotically strictly pseudocontractive mapping in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the two sets.

VECTOR EQUILIBRIUM PROBLEMS FOR TRIFUNCTION IN MEASURABLE SPACE AND ITS APPLICATIONS

  • RAM, TIRTH;KHANNA, ANU KUMARI
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.577-585
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    • 2022
  • In this work, we introduced and study vector equilibrium problems for trifunction in measurable space (for short, VEPMS). The existence of solutions of (VEPMS) are obtained by employing Aumann theorem and Fan KKM lemma. As an application, we prove an existence result for vector variational inequality problem for measurable space. Our results in this paper are new which can be considered as significant extension of previously known results in the literature.

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.

Convergence Theorem for Finding Common Fixed Points of N-generalized Bregman Nonspreading Mapping and Solutions of Equilibrium Problems in Banach Spaces

  • Jolaoso, Lateef Olakunle;Mewomo, Oluwatosin Temitope
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.523-558
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    • 2021
  • In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature.

Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

  • Dhananjaya, H.R.;Pandey, P.C.;Nagabhushanam, J.;Othamon, Ismail
    • Structural Engineering and Mechanics
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    • v.40 no.1
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    • pp.121-148
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    • 2011
  • Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.