ABSTRACT
In the present chapter, we investigate a class of Banach algebras satisfying
the condition (P) (see Definition 1.5.2). The central goal is to prove some new fixed point theorems under a weak topology setting for maps acting on
a nonempty, closed, and convex subset of a Banach algebra satisfying or not
the condition (P). Our main conditions are formulated in terms of weak sequential continuity, dealing with three nonlinear operators. Moreover, no weak
continuity conditions are required for this work. In addition, some fixed results
using the notion of WC-Banach algebras are discussed.
