Perturbed algorithms for solving nonlinear relaxed cocoercive operator equations with general A-monotone operators in Banach spaces

Based on the notion of general A-monotonicity, the new proximal mapping technique and Alber’s inequalities, a new class of nonlinear relaxed cocoercive operator equations with general A-monotone operators in Banach spaces is introduced and studied. Further, we also discuss the convergence and stability of a new perturbed iterative algorithm with errors for solving this class of nonlinear operator equations in Banach spaces. Since general A-monotonicity generalizes general H-monotonicity (and in turn, generalizes A-monotonicity, H-monotonicity and maximal monotonicity), our results improve and generalize the corresponding results of recent works.

Research highlights►The new proximal mapping technique and Alber’s inequalities were used. ►We studied a new class of nonlinear relaxed cocoercive operator equations. ►We discussed the convergence and stability of the perturbed iterative algorithms. ►General A-monotonicity in Banach spaces generalizes the existed monotonicity. ►The results improve and generalize the corresponding results of recent works.