A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

a new class of nonlinear set-valued variationalinclusions involving $(a,eta)$-monotone mappings in a banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(a,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.