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We introduce and study a new system of nonlinear variational-like inclusions involving  Open image in new window - Open image in new window -maximal monotone operators, strongly monotone operators,  Open image in new window -strongly monotone operators, relaxed monotone operators, cocoercive operators,  Open image in new window -relaxed cocoercive operators,  Open image in new window - Open image in new window -relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique associated with  Open image in new window - Open image in new window -maximal monotone operators and Banach contraction principle, we demonstrate the existence and uniqueness of solution for the system of nonlinear variational-like inclusions. The results presented in the paper improve and extend some known results in the literature.

The Solvability of a New System of Nonlinear Variational-Like Inclusions