# Solvability of a Class of Generalized System of Variational Inclusion Problems Involving \(\oplus\) Operation

## DOI:

https://doi.org/10.26713/cma.v14i5.2099## Keywords:

Variational inclusion, ⊕ operation, Resolvent operator, Algorithm, Convergence## Abstract

In this paper, a new type of operator known as \((\alpha,\rho)\)-XOR-NODSM operator and its associated resolvent operator is introduced. Further, some important properties of the resolvent operator associated with the \((\alpha,\rho)\)-XOR-NODSM operator, supported by a well constructed example, have been given. As an application, we have considered a generalized system of variational inclusion problems involving XOR operator in the setting of real ordered positive Hilbert space. Using the resolvent operator technique, we have proved the existence of solution for the system considered. Furthermore, the approximation solvability of the generalized system of variational inclusion problems involving the XOR operator has been studied. The results presented in this paper can be treated as the refinement and generalization of many known results present in the literature in this direction.

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*Communications in Mathematics and Applications*,

*14*(5), 1585–1601. https://doi.org/10.26713/cma.v14i5.2099

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