Variational inclusions with a general [formula omitted]-monotone operator in Banach spaces

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In this paper, we introduce a new class of operator–general H -monotone operators in Banach space. We define a proximal mapping associated with the general H -monotone operator and show its Lipschitz continuity. We also consider a new class of variational inclusions involving these general H -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.