Modified forward-backward splitting midpoint method with superposition perturbations for the sum of two kinds of infinite accretive mappings and its applications

Abstract

Abstract In a real uniformly convex and p-uniformly smooth Banach space, a modified forward-backward splitting iterative algorithm is presented, where the computational errors and the superposition of perturbed operators are considered. The iterative sequence is proved to be convergent strongly to zero point of the sum of infinite m-accretive mappings and infinite θ i $\theta_{i}$ -inversely strongly accretive mappings, which is also the unique solution of one kind variational inequalities. Some new proof techniques can be found, especially, a new inequality is employed compared to some of the recent work. Moreover, the applications of the newly obtained iterative algorithm to integro-differential systems and convex minimization problems are exemplified.

Keywords

• p-uniformly smooth Banach space
• θ i $\theta_{i}$ -inversely strongly accretive mapping
• γ i $\gamma_{i}$ -strongly accretive mapping
• μ i $\mu_{i}$ -strictly pseudo-contractive mapping
• perturbed operator