Relaxed iterative methods for an infinite family of d-accretive mappings in a Banach space and their applications
Journal of Nonlinear Functional Analysis · 2018
In this paper, d-accretive mappings, which belong to accretive-type mappings but are different from m-accretive mappings, are studied.Some relaxed projection iterative algorithms for an infinite family of d-accretive mappings are constructed in a real uniformly convex and uniformly smooth Banach space.The iterative sequences are proved to be strongly convergent to a common zero point of the family of d-accretive mappings.Compared to the related work, the construction of the iterative algorithms are simpler and easily realized.Moreover, a kind of generalized (p, q)-Laplacian parabolic systems is exemplified.The example also emphasizes the importance of the study on d-accretive mappings and sets up a relationship between iterative algorithms and nonlinear systems.