• Title, Summary, Keyword: equilibrium problem

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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].

NONLINEAR ALGORITHMS FOR A COMMON SOLUTION OF A SYSTEM OF VARIATIONAL INEQUALITIES, A SPLIT EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEMS

  • Jeong, Jae Ug
    • Korean Journal of Mathematics
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    • v.24 no.3
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    • pp.495-524
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    • 2016
  • In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

A NEW ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEM AND FINDING COMMON FIXED POINTS OF BREGMAN STRONGLY NONEXPANSIVE MAPPINGS

  • Biranvand, Nader;Darvish, Vahid
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.777-798
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    • 2018
  • In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE

  • DJAFARI-ROUHANI, BEHZAD;FARID, MOHAMMAD;KAZMI, KALEEM RAZA
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.89-114
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    • 2016
  • In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

LINEAR STABILITY OF TRIANGULAR EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL RESTRICTED THREE BODY PROBLEM WITH TRIAXIAL RIGID BODIES, WITH THE BIGGER ONE AN OBLATE SPHEROID AND SOURCE OF RADIATION

  • KUMAR, AVDHESH;ISHWAR, B.
    • Publications of The Korean Astronomical Society
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    • v.30 no.2
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    • pp.297-299
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    • 2015
  • In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

WEAK AND STRONG CONVERGENCE THEOREMS FOR A SYSTEM OF MIXED EQUILIBRIUM PROBLEMS AND A NONEXPANSIVE MAPPING IN HILBERT SPACES

  • Plubtieng, Somyot;Sombut, Kamonrat
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.375-388
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    • 2013
  • In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.

ITERATIVE METHODS FOR GENERALIZED EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS

  • Cho, Sun-Young;Kang, Shin-Min;Qin, Xiaolong
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.51-65
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    • 2011
  • In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

AN ITERATIVE METHOD FOR SOLVING EQUILIBRIUM PROBLEM FIXED POINT PROBLEM AND GENERALIZED VARIATIONAL INEQUALITIES PROBLEM

  • Zhang, Lijuan;Li, Juchun
    • East Asian mathematical journal
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    • v.27 no.5
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    • pp.527-538
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    • 2011
  • In this paper, we introduce a new iterative scheme for finding a common element of the set of an equilibrium problem, the set of fixed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for ${\alpha}$-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.

WEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS AND NONSPREADING MAPPINGS IN HILBERT SPACES

  • Jiang, Li;Su, Yongfu
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.505-512
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    • 2012
  • In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mappings and nonspreading mappings and the set of solution of an equilibrium problem on the setting of real Hilbert spaces.