Abstract:
In this paper, we introduce a new class of monotone generalized
nonexpansive mappings and we establish some weak and strong convergence theorem
for a newly proposed iterative process in the frame work of an ordered Banach
space. This class of mappings is wider than the class of nonexpansive mappings,
mean nonexpansive mappings and mappings satisfying condition (C). In addition,
we establish that our newly proposed iterative process is faster than some existing
iterative process in the literature. Finally, we provide an application to the space
of L1([0, 1]) and to nonlinear integral equations. The results obtained in this paper
improve, extend and unify some related results in the literature.