• Korean Journal of Mathematics
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• v.25 no.3
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• pp.359-377
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• 2017

In this paper, we consider a system of generalized nonlinear ordered variational inclusions in real ordered Banach spaces and define an iterative algorithm for a solution of our problems. By using the resolvent operator techniques to prove an existence result for the solution of the system of generalized nonlinear ordered variational inclusions and discuss convergence of sequences suggested by the algorithms.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.103-119
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• 2021

In this article, we study a system of generalized set-valued parametric ordered variational inclusion problems with operator ⊕ in ordered Banach spaces. We introduce the concept of the resolvent operator associated with (α, λ)-ANODSM set-valued mapping and establish the existence theorem of solution for the system of generalized set-valued parametric ordered variational inclusion problems in ordered Banach spaces. In order to prove the existence of solution, we suggest an iterative algorithm and discuss the convergence analysis under some suitable mild conditions.