• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.101-113
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• 2000

In this paper, we introduce and study a new class of variational inclusions, called the set-valued quasi variational inclusions. The resolvent operator technique is used to establish the equivalence between the set-valued variational inclusions and the fixed point problem. This equivalence is used to study the existence of a solution and to suggest a number of iterative algorithms for solving the set-valued variational inclusions. We also study the convergence criteria of these algorithms.

• East Asian mathematical journal
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• v.31 no.3
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• pp.383-391
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• 2015

We considered a new system of generalized nonlinear mixed variational inclusions in Hilbert spaces and define an iterative method for finding the approximate solutions of this class of system of generalized nonlinear mixed variational inclusions. We also established that the approximate solutions obtained by our algorithm converges to the exact solutions of a new system of generalized nonlinear mixed variational inclusions.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.493-506
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• 2005

In this paper, we study the behavior and sensitivity analysis of the solution set for a system of parametric generalized nonlinear mixed quasi-variational inclusions in Banach spaces. By using some new and innovative technique, existence theorem for the system of parametric generalized nonlinear mixed quasi-variational inclusions in $L_p(p\ge2$ spaces is established. Our results improve the known result of Agarwal et al.[1].

• Kyungpook Mathematical Journal
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• v.59 no.1
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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.

• Korean Journal of Mathematics
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• v.26 no.1
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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.

• East Asian mathematical journal
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• v.28 no.1
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• pp.37-47
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• 2012

In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• East Asian mathematical journal
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• v.26 no.5
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• pp.671-680
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• 2010

A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variational inclusions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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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.