### Existence and algorithm of solutions for a new system of generalised variational inclusions involving relaxed Lipschitz mappings

#### Abstract

We consider a new system for generalized variational inclusions in Hilbert spaces and define an iterative algorithm for finding the approximate solutions of this class of system of variational inclusions. We also establish that the approximate solutions obtained by our algorithm converge to the exact solution of new system of generalized variational inclusions. One can explore the role of our system of generalized variational inclusions for solving various known equilibrium problem and other related problems.

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DOI: http://dx.doi.org/10.21914/anziamj.v49i0.55

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