• 제목/요약/키워드: variational inclusion

검색결과 47건 처리시간 0.018초

A MODIFIED PROXIMAL POINT ALGORITHM FOR SOLVING A CLASS OF VARIATIONAL INCLUSIONS IN BANACH SPACES

  • LIU, YING
    • Journal of applied mathematics & informatics
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    • 제33권3_4호
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    • pp.401-415
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    • 2015
  • In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

SENSITIVITY ANALYSIS FOR A NEW SYSTEM OF VARIATIONAL INEQUALITIES

  • Jeong, Jae-Ug
    • 대한수학회논문집
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    • 제25권3호
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    • pp.427-441
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    • 2010
  • In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of generalized parametric multi-valued variational inclusions with (A, $\eta$)-accretive mappings in q-uniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

STRONG CONVERGENCE OF EXTENDED GENERAL VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS

  • Chen, Jun-Min;Zhang, Li-Juan;He, Zhen
    • East Asian mathematical journal
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    • 제26권1호
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    • pp.59-67
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    • 2010
  • In this paper, we suggest and analyze some three step iterative scheme for finding the common elements of the set of the solutions of the extended general variational inequalities involving three operators and the set of the fixed points of nonexpansive mappings. We also consider the convergence analysis of suggested iterative schemes under some mild conditions. Since the extended general variational inequalities include general variational inequalities and several other classes of variational inequalities as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the previously known results.

Iterative Algorithm for a New System of Variational Inclusions with B-monotone Operators in Banach Spaces

  • Lee, Sang Keun;Jeong, Jae Ug
    • Kyungpook Mathematical Journal
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    • 제53권3호
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    • pp.307-318
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    • 2013
  • In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with B-monotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm for this system of variational inclusions. The results presented in this paper extend and improve some known results in the literature.

INERTIAL EXTRAPOLATION METHOD FOR SOLVING SYSTEMS OF MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS USING BREGMAN DISTANCE APPROACH

  • Hammed A. Abass;Ojen K. Narain;Olayinka M. Onifade
    • Nonlinear Functional Analysis and Applications
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    • 제28권2호
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    • pp.497-520
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    • 2023
  • Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

NEW PROXIMAL ALGORITHMS FOR A CLASS OF $(A,\;{\eta})-ACCRETIVE$ VARIATIONAL INCLUSION PROBLEMS WITH NON-ACCRETIVE SET-VALUED MAPPINGS

  • Lan, Heng-You
    • Journal of applied mathematics & informatics
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    • 제25권1_2호
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    • pp.255-267
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    • 2007
  • In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.

A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuan-Zhi;Fang, Jin-Xuan
    • 대한수학회보
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    • 제40권3호
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    • pp.385-397
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    • 2003
  • In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $x^{*},\;y^{*},\;z^{*}\;\in\;E$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $E\;{\rightarrow}\;E,\;{\theta}$ is zero element in Banach space E, and A : $E\;{\rightarrow}\;{2^E}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.

A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuanzhi;Yang, Qing
    • 대한수학회논문집
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    • 제25권1호
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    • pp.129-137
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    • 2010
  • In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

GENERAL ITERATIVE ALGORITHMS FOR MONOTONE INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS

  • Jung, Jong Soo
    • 대한수학회지
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    • 제58권3호
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    • pp.525-552
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    • 2021
  • In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

A PROXIMAL POINT ALGORITHM FOR SOLVING THE GENERAL VARIATIONAL INCLUSIONS WITH M(·, ·)-MONOTONE OPERATORS IN BANACH SPACES

  • Chen, Junmin;Wang, Xian;He, Zhen
    • East Asian mathematical journal
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    • 제29권3호
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    • pp.315-326
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    • 2013
  • In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.