Sentence examples for mappings in normal from inspiring English sources

One of the main results of Huang and Zhang in [1] is fixed point theorems for contractive mappings in normal cone spaces.

Huang and Zhang [1] recently have introduced the concept of cone metric space, where the set of real numbers is replaced by an ordered Banach space, and they have established some fixed point theorems for contractive type mappings in a normal cone metric space.

The purpose of the present paper is to extend and generalise the above Theorems 1.1 and 1.2 for two mappings in non-normal cone metric spaces and by removing the requirement of D(T u, u,... u), T v, v,... v)) < d u, v), for all u, v ∈ X for uniqueness of the fixed point, which in turn will extend and generalise the results of [3, 4].

Cho and Bae [18] presented the result of [15] for multivalued mappings in cone metric spaces with normal cone.

We first state and prove a fixed point result of order-Lipschitz mappings in Banach algebras with non-normal cones as follows.

By introducing the concept of Picard-complete and using the sandwich theorem in the sense of w-convergence established in [4], we first prove some fixed point theorems of order-Lipschitz mappings in Banach algebras with non-normal cones.

In this paper, by introducing the concept of Picard-completeness and using the sandwich theorem in the sense of w-convergence, we first prove some fixed point theorems of order-Lipschitz mappings in Banach algebras with non-normal cones which improve the result of Sun's since the normality of the cone was removed.

We modify the normal Mann iterative process to have strong convergence for a finite family nonexpansive mappings in the framework of Banach spaces without any commutative assumption.

He published his first volume of poetry, called Mappings, in 1980.

The first problem I identified involved the necessity of 'normal structure' in the fundamental existence theorem for nonexpansive mappings in weakly compact sets.

With the mappings in Eqs.