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A new three-step iterative algorithm for approximating the zero point of the sum of an infinite family of m-accretive mappings and an infinite family of $\mu_{i}$-inversely strongly accretive mappings in a real q-uniformly smooth and uniformly convex Banach space is presented. The computational error in each step is being considered. A strong convergence theorem is proved by means of some new techniques, which extend the corresponding work by some authors. The relationship between the zero point of the sum of an infinite family of m-accretive mappings and an infinite family of $\mu_{i}$-inversely strongly accretive mappings and the solution of one kind variational inequalities is investigated. As an application, an integro-differential system is exemplified, from which we construct an infinite family of m-accretive mappings and an infinite family of $\mu_{i}$-inversely strongly accretive mappings. Moreover, the iterative sequence of the solution of the integro-differential systems is obtained.

fixed point theory and applications

A new iterative algorithm for the sum of infinite m-accretive mappings and infinite $\mu_{i}$-inversely strongly accretive mappings and its applications to integro-differential systems