Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

Abstract EN

We introduce a new generalized resolvent in a Banach space and discuss some of its properties.

Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping.

Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.