Sentence examples for mappings for which from inspiring English sources

It is clear that in Hilbert spaces the important class of nonexpansive mappings (mappings for which ) is a subclass of the class of strictly pseudocontractive maps.

It is clear that nonexpansive mappings and mappings for which (5.1) holds satisfy (5.9) and (5.10).

Suppose that and are mappings for which there exists such that (2.1).

In this remarkable paper, the mappings, for which the existence and uniqueness of a fixed point were discussed, do not need to be continuous.

Very recently, Gu and Yin [38] obtained some common fixed point theorems of three pairs of mappings for which only two pairs need to satisfy the common ( E. A ) property in the framework of G-metric spaces.

Next we present two examples of complete quasi-metric spaces ((X,d)) with appropriate d-Caristi mappings, for which Caristi's fixed point theorem cannot be applied to the metric space ((X,d^{s})).

Let be mappings with for which there exists a function such that (3.2). (3.3).

Let be mappings with for which there exists a function satisfying (3.2)–(3.2).

However, we observe that there are many multivalued mappings T for which neither T nor P T is nonexpansive.

Let (K_{1}) be the smallest open set in K containing (K_{0}) and, considering the continuity of T, we conclude that condition (5) is satisfied by nonexpansive mappings T for which (operatorname{Fix}(T) neq emptyset).

Let us consider (boldsymbol{Psi}_{mathbf{P}}) ((Phi_{P}subsetPsi_{P} subset Phi)) consisting of mappings φ for which every sequence ((a_{n})_{n inmathbb{N}}) such that (0 < a_{n+1}leq varphi (a_{n} )), (n inmathbb{N}) converges to zero.