• 제목/요약/키워드: variational inclusion

검색결과 47건 처리시간 0.017초

A HYBRID PROJECTION METHOD FOR RELAXED COCOERCIVE MAPPINGS AND STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

  • Liu, Ying
    • East Asian mathematical journal
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    • 제28권3호
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    • pp.305-320
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    • 2012
  • The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

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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    • 제29권3_4호
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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.

Random completley generalized nonlinear variational inclusions with non-compact valued random mappings

  • Huang, Nan-Jing;Xiang Long;Cho, Yeol-Je
    • 대한수학회보
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    • 제34권4호
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    • pp.603-615
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    • 1997
  • In this paper, we introduce and study a new class of random completely generalized nonlinear variational inclusions with non-compact valued random mappings and construct some new iterative algorithms. We prove the existence of random solutions for this class of random variational inclusions and the convergence of random iterative sequences generated by the algorithms.

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RELAXED PROXIMAL POINT ALGORITHMS BASED ON A-AXIMAL RELAXED MONOTONICITY FRAMEWORKS WITH APPLICATIONS

  • Agarwal, Ravi P.;Verma, Ram U.
    • East Asian mathematical journal
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    • 제27권5호
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    • pp.545-555
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    • 2011
  • Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.

GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

  • Verma, Ram U.
    • 대한수학회논문집
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    • 제26권4호
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    • pp.685-693
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    • 2011
  • General framework for proximal point algorithms based on the notion of (A, ${\eta}$)-maximal monotonicity (also referred to as (A, ${\eta}$)-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to (A, ${\eta}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

SENSITIVITY ANALYSIS FOR A SYSTEM OF GENERALIZED NONLINEAR MIXED QUASI-VARIATIONAL INCLUSIONS WITH (A, η)-ACCRETIVE MAPPINGS IN BANACH SPACES

  • Jeong, Jae-Ug;Kim, Soo-Hwan
    • 대한수학회보
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    • 제46권6호
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    • pp.1175-1188
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    • 2009
  • In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of parametric generalized nonlinear mixed quasi-variational inclusions with (A, ${\eta$)-accretive mappings in quniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR A CLASS OF NONLINEAR SET-VALUED VARIATIONAL INCLUSIONS

  • Ding, Xie Ping;Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • 제25권1호
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    • pp.19-35
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    • 2017
  • In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.