• 제목/요약/키워드: variational

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GENERALIZED VECTOR MINTY'S LEMMA

  • Lee, Byung-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제19권3호
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    • pp.281-288
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    • 2012
  • In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

MINTY'S LEMMA FOR STRONG IMPLICIT VECTOR VARIATIONAL INEQUALITY SYSTEMS

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제15권4호
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    • pp.423-432
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    • 2008
  • In this paper, we consider a new Minty's Lemma for strong implicit vector variational inequality systems and obtain some existence results for systems of strong implicit vector variational inequalities which generalize some results in [1].

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EXISTENCE RESULTS FOR VECTOR NONLINEAR INEQUALITIES

  • Lee, Suk-Jin;Lee, Byung-Soo
    • 대한수학회논문집
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    • 제18권4호
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    • pp.737-743
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    • 2003
  • The purpose of this paper is to consider some existence results for vector nonlinear inequalities without any monotonicity assumption. As consequences of our main result, we give some existence results for vector equilibrium problem, vector variational-like inequality problem and vector variational inequality problems as special cases.

Approximation Solvability for a System of Nonlinear Variational Type Inclusions in Banach Spaces

  • Salahuddin, Salahuddin
    • Kyungpook Mathematical Journal
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    • 제59권1호
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    • pp.101-123
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    • 2019
  • In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

ITERATING A SYSTEM OF SET-VALUED VARIATIONAL INCLUSION PROBLEMS IN SEMI-INNER PRODUCT SPACES

  • Shafi, Sumeera
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제29권4호
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    • pp.255-275
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    • 2022
  • In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

APPROXIMATE PROJECTION ALGORITHMS FOR SOLVING EQUILIBRIUM AND MULTIVALUED VARIATIONAL INEQUALITY PROBLEMS IN HILBERT SPACE

  • Khoa, Nguyen Minh;Thang, Tran Van
    • 대한수학회보
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    • 제59권4호
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    • pp.1019-1044
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    • 2022
  • In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

SINGULARITY FORMATION FOR A NONLINEAR VARIATIONAL SINE-GORDON EQUATION IN A MULTIDIMENSIONAL SPACE

  • Fengmei Qin;Kyungwoo Song;Qin Wang
    • 대한수학회보
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    • 제60권6호
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    • pp.1697-1704
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    • 2023
  • We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

CONVERGENCE OF PARALLEL ITERATIVE ALGORITHMS FOR A SYSTEM OF NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES

  • JEONG, JAE UG
    • Journal of applied mathematics & informatics
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    • 제34권1_2호
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    • pp.61-73
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    • 2016
  • In this paper, we consider the problems of convergence of parallel iterative algorithms for a system of nonlinear variational inequalities and nonexpansive mappings. Strong convergence theorems are established in the frame work of real Banach spaces.

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES FOR SET-VALUED MAPPINGS

  • Lee, Suk-Jin;Lee, Byung-Soo
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제10권4호
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    • pp.225-232
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    • 2003
  • In this paper, we consider the existence of the solutions to the generalized vector variational-type inequalities for set-valued mappings on Hausdorff topological vector spaces using Fan's geometrical lemma.

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