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In this paper, we present a new iterative algorithm with errors to solve the problems of finding zeros of the sum of finitely many m-accretive operators and finitely many α-inversely strongly accretive operators in a real smooth and uniformly convex Banach space. Strong convergence theorems are established, which extend the corresponding works given by some authors. Moreover, the relationship among the zero of the sum of m-accretive operator and α-inversely strongly accretive operator, the solution of one kind variational inequality, and the solution of the capillarity equation is investigated.

fixed point theory and applications

A new iterative algorithm for the sum of two different types of finitely many accretive operators in Banach space and its connection with capillarity equation