Variational inclusions with a general HH-monotone operator in Banach spaces

In this paper, we introduce a new class of operator–general HH-monotone operators in Banach space. We define a proximal mapping associated with the general HH-monotone operator and show its Lipschitz continuity. We also consider a new class of variational inclusions involving these general HH-monotone operators and constructed a new iterative algorithm for solving the variational inclusion in Banach spaces. Under some suitable conditions, we prove the convergence of the iterative sequence generated by the algorithm.