Sentence examples for mappings to have from inspiring English sources

In this paper, we first show that this condition is necessary for the considered mappings to have a fixed point.

Next, we provide some examples of universally inductive sets and investigate some more practical conditions for set-valued mappings to have fixed point in partially ordered topological spaces, where the continuity condition is not applied to the considered mappings.

Remark 2.66 Besides commutativity of the mappings the notion of non-trivial OWC requires the mappings to have a coincidence point and, therefore, imposes a very strong condition on the mappings.

In 2012, Chang et al. [1] used the following modified Halpern-type iteration algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings to have the strong convergence under a limit condition only in the framework of Banach spaces.

The purpose of this paper is to modify the Halpern and Mann-type iteration algorithm for a family of totally quasi-ϕ-asymptotically nonexpansive nonself mappings to have the strong convergence under a limit condition only in the framework of Banach spaces.

Then { x n } converges strongly to a fixed point of T. The purpose of this paper is to introduce the following Mann-type implicit iteration process associated with a family of continuous hemicontractive mappings to have a strong convergence in the setting of Hilbert spaces.

Along this line, Li and Ok [2] explore the order-preserving of generalized metric projection operator and study the existence of maximum (minimum) solutions to (operatorname{GVI}(C,Gamma)) on Banach lattices, where the considered mappings are required to have topped (bottomed) values.

On the other hand, the following fixed point iteration processes have been extensively studied by many authors for approximating either fixed points of nonlinear mappings (when these mappings are already known to have fixed points) or solutions of nonlinear operator equations.

The mappings and are said to have an approximate coincidence point property provided (2.10).

These clarify how perturbations to the observation functions can be constructed and highlight why

Recall that a self-mapping T is said to have the property P if (operatorname{Fix}(T^{n}) = F(T)) for every (ninmathbb{N}).