Sentence examples for mappings to prove from inspiring English sources

Let us apply cross mappings to prove the following.

In this section, we use the iterative process (1.4) for nonexpansive mappings to prove some convergence theorems.

Kim [14] used hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings to prove the strong convergence theorems.

Furthermore, Murthy et al. [18] generalized the concept of cyclic weak φ-contraction to cyclic weak -contraction and utilized these contractive mappings to prove a fixed point theorem in a G-complete fuzzy metric space.

The idea of the definition of a total asymptotically nonexpansive mappings is to unify various definitions of classes of mappings associated with the class of asymptotically nonexpansive mappings and to prove a general convergence theorems applicable to all these classes of nonlinear mappings.

The purpose of this paper is first to introduce the class of total asymptotically nonexpansive nonself mappings and to prove the demiclosed principle for such mappings in CAT ( 0 ) spaces.

It is our purpose in this paper first to introduce the class of total asymptotically nonexpansive nonself mappings and to prove the demiclosed principle for such mappings in CAT ( 0 ) spaces.

The purpose of this article is to present a simple projection algorithm for a countable family of weak relatively nonexpansive mappings and to prove strong convergence theorems in Banach spaces.

The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove some Δ-convergence theorems of the mixed type iteration process to approximating a common fixed point for two asymptotically nonexpansive mappings and two total asymptotically nonexpansive mappings in hyperbolic spaces.

The purpose of this paper is to introduce the concepts of total asymptotically nonexpansive mappings and to prove some Δ-convergence theorems of the mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive mappings and two total asymptotically nonexpansive mappings in hyperbolic spaces.

The purpose of this paper is to construct a new iteration scheme of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and to prove some strong and weak convergence theorems for the new iteration scheme in uniformly convex Banach spaces.