• 제목/요약/키워드: variational inclusion

검색결과 47건 처리시간 0.019초

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.

AN ITERATIVE ALGORITHM FOR EXTENDED GENERALIZED NONLINEAR VARIATIONAL INCLUSIONS FOR RANDOM FUZZY MAPPINGS

  • Dar, A.H.;Sarfaraz, Mohd.;Ahmad, M.K.
    • Korean Journal of Mathematics
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    • 제26권1호
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    • pp.129-141
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    • 2018
  • In this slush pile, we introduce a new kind of variational inclusions problem stated as random extended generalized nonlinear variational inclusions for random fuzzy mappings. We construct an iterative scheme for the this variational inclusion problem and also discuss the existence of random solutions for the problem. Further, we show that the approximate solutions achieved by the generated scheme converge to the required solution of the problem.

Sensitivity Analysis for Generalized Nonlinear Implicit Quasi-variational Inclusions

  • Jeong, Jae Ug
    • Kyungpook Mathematical Journal
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    • 제46권3호
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    • pp.345-356
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    • 2006
  • In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a new class of parametric generalized nonlinear implicit quasi-variational inclusion problem in $L_p(p{\geq}2)$ spaces. The results presented in this paper are new and generalize many known results in this field.

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FUZZY NONLINEAR RANDOM VARIATIONAL INCLUSION PROBLEMS INVOLVING ORDERED RME-MULTIVALUED MAPPING IN BANACH SPACES

  • Kim, Jong Kyu;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • 제34권1호
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    • pp.47-58
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    • 2018
  • In this paper, we consider a fuzzy nonlinear random variational inclusion problems involving ordered RME-multivalued mapping in ordered Banach spaces. By using the random relaxed resolvent operator and its properties, we suggest an random iterative algorithm. Finally both the existence of the random solution of the original problem and the convergence of the random iterative sequences generated by random algorithm are proved.

VARIATIONAL-LIKE INCLUSION SYSTEMS VIA GENERAL MONOTONE OPERATORS WITH CONVERGENCE ANALYSIS

  • Dadashi, Vahid;Roohi, Mehdi
    • East Asian mathematical journal
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    • 제26권1호
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    • pp.95-103
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    • 2010
  • In this paper using Lipschitz continuity of the resolvent operator associated with general H-maximal m-relaxed $\eta$-monotone operators, existence and uniqueness of the solution of a variational inclusion system is proved. Also, an iterative algorithm and its convergence analysis is given.

GENERAL NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE OPERATOR IN HILBERT SPACES

  • Liu, Zeqing;Zheng, Pingping;Cai, Tao;Kang, Shin-Min
    • 대한수학회보
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    • 제47권2호
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    • pp.263-274
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    • 2010
  • In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.

ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING

  • Liu, Zeqing;Chen, Zhengsheng;Shim, Soo-Hak;Kang, Shin-Min
    • 대한수학회지
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    • 제45권5호
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    • pp.1323-1339
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    • 2008
  • In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

A HYBRID PROXIMAL POINT ALGORITHM AND STABILITY FOR SET-VALUED MIXED VARIATIONAL INCLUSIONS INVOLVING (A, ${\eta}$)-ACCRETIVE MAPPINGS

  • Kim, Jong-Kyu;Li, Hong Gang
    • East Asian mathematical journal
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    • 제26권5호
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    • pp.703-714
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    • 2010
  • A new class of nonlinear set-valued mixed variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces is introduced and studied, which includes many kind of variational inclusion (inequality) and complementarity problems as special cases. By using the resolvent operator associated with (A, ${\eta}$)-accretive operator due to Lan-Cho-Verma, the existence of solution for this kind of variational inclusion is proved, and a new hybrid proximal point algorithm is established and suggested, the convergence and stability theorems of iterative sequences generated by new iterative algorithms are also given in q-uniformly smooth Banach spaces.

A RANDOM GENERALIZED NONLINEAR IMPLICIT VARIATIONAL-LIKE INCLUSION WITH RANDOM FUZZY MAPPINGS

  • Khan, F.A.;Aljohani, A.S.;Alshehri, M.G.;Ali, J.
    • Nonlinear Functional Analysis and Applications
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    • 제26권4호
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    • pp.717-731
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    • 2021
  • In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.