Sentence examples for mappings as generalized from inspiring English sources

Therefore, it is natural to call these mappings as "generalized nonexpansive mappings".

nonexpansive if Vert Tx - Ty Vert leq Vert x - y Vert, for all (x, y in C); quasi-nonexpansive if Vert Tx - p Vert leq Vert x - p Vert, for each (p in F(T)) and for all (xin C), where (F(T)= {x in C; Tx = x }) denotes the set of fixed points of T. In 2008, Suzuki [1] introduced a class of single-valued mappings, called Suzuki-generalized nonexpansive mappings, as follows.

This article presents best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric spaces.

The main objective of this article is to present, in the framework of complete metric spaces, a best proximity point theorem for a new family of non-self mappings, known as generalized contractions, thereby computing an optimal approximate solution to the equation S x = x, where S is a generalized contraction.

Define two mappings as (2.25).

We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan [1] generalized to the case of two mappings in Hilbert spaces without closedness of C. First we introduce further generalized hybrid mappings as another generalization of normally generalized hybrid mappings.

The existence of common fixed points for weakly compatible self-mappings as well as Banach operator pairs under certain generalized contractions in a convex metric space is also established.

The aim of this work is to extend the notion of weakly isotone increasing mappings to multivalued and present common endpoint theorems for T -weakly isotone increasing multivalued mappings satisfying generalized -weak contractive as well as almost contractive inequalities in complete partially ordered metric spaces.

Define mappings between generalized archetypes and specialized archetypes to facilitate data query.

Hojo et al. [35] also studied the fixed point theorems for N-generalized hybrid mappings in Hilbert spaces and provided an example of N-generalized hybrid mappings which are not generalized hybrid mappings as follows.

Moreover, it is natural to extend such powerful results to generalized nonexpansive mappings as a mean of testing the limit of the theory of nonexpansive mappings.