It is also known that the fixed point problems for isotone mappings are easier than for mixed monotone mappings.
It is well known that the fixed point problems for isotone mappings are easier than that of mixed monotone mappings.
It is known that the degree of finite dimensional mappings is easier to calculate.
Still, some of the fundamental difficulties with the structure-mapping approach are easiest to appreciate if we focus on the early version.
On the other hand, for each n ∈ N, since J λ n, and T r n are firmly nonexpansive mappings, it is easy to see that J λ n and T r n are 1 2 averaged.
On the other hand, for each n ∈ N, J ρ n G 1 is a firmly nonexpansive mappings, it is easy to see that J ρ n G 1 is 1 2 -averaged.
Proof Let α, β : X × X → [ 0, + ∞ ) be the mapping defined by α ( x, y ) = β ( x, y ) = 1 for all x, y ∈ X. Then T is -contractive mappings. It is easy to show that all the hypotheses of Theorems 2.1 and 2.2 are satisfied. Consequently, T has a unique fixed point. □. Corollary 4.2 (Rhoades [17]).
It is easy to verify that these mappings are continuous (although the mapping (pmapsto f_{p}) is not continuous for (p=0)), so they are exponentially convex.
It is easy to see that nonexpansive mappings are Lipschitz continuous; however, the quasi-nonexpansive mapping is discontinuous on its domain generally.
It is easy to see that these mappings are continuous, so they are exponentially convex.
