Sentence examples for mappings and studied from inspiring English sources
Alber et al. [13] introduced a more general class of asymptotically nonexpansive mappings called total asymptotically nonexpansive mappings and studied the methods of approximation of fixed points.
Takahashi et al. [1 7] gave the following definitions of nonlinear mappings and studied the existence and convergence theorems of fixed points for these mappings.
They introduced the class of probabilistic G-contraction single-valued mappings and studied the existence of fixed points for such mappings.
Albert et al. [4] introduced a more general class of asymptotically nonexpansive mappings called total asymptotically nonexpansive mappings and studied methods of approximation of fixed points of mappings belonging to this class.
In [24], the authors introduced the Ishikawa iterative scheme for two mappings and studied the strong convergence of this scheme to a common fixed point of the two mappings.
Afterwards, Nieto and Rodríguez-López [19] extended the results of Ran and Reurings for nondecreasing mappings and studied the existence and uniqueness of solutions for a first-order ordinary differential equation with periodic boundary conditions.
We introduce a new class of asymptotically nonexpansive mappings and study approximating methods for finding their fixed points.
In order to show more specific and qualitative results, we apply the mappings and study a snake robot with two joints (c.f. Fig. 3).
Motivated by this observation and those previous works, we are interested in introducing the concept of graph-preserving for multi-valued mappings and study their fixed point theorem in a complete metric space endowed with a graph.
In this paper, we introduce a class of totally quasi-ϕ-asymptotically nonexpansive nonself mappings and study the strong convergence under a limit condition only in the framework of Banach spaces.
In a recent paper [10], the authors investigate the existence of a fixed point of asymptotic pointwise nonexpansive mappings and study the convergence of the modified Mann iteration in hyperbolic metric spaces.
