Sentence examples for mapping defined on from inspiring English sources

Lin proved that (ell_{1}) endowed with this norm verifies the fixed point property for nonexpansive mappings, that is, every (|!|!|cdot|!|!| -nonexpansive mapping defined on a closed convex bounded subset of (ell_{1}) into itself has a fixed point.

Rhoades [9] considered this class of mappings in the setup of metric spaces and proved that a weakly contractive mapping defined on a complete metric space has a unique fixed point.

They called such mappings locally gross direction preserving and proved that every locally gross direction preserving mapping defined on a nonempty polytope (the convex hull of a finite subset of ) has a fixed point.

Rhoades [14] generalized the Banach contraction principle by considering this class of mappings in the setup of metric spaces and proved that every weakly contractive mapping defined on a complete metric space has a unique fixed point.

Let be a mapping defined on a closed subset of a Banach space.

Lemma 5.1 A nonexpansive mapping defined on a CAT ( 1 ) space is Δ-demiclosed.

We know that if X is a complete metric space, every Kannan self-mapping defined on X has a unique fixed point [2].

Several problems can be changed to equations of the form T x = x, where T is a given self-mapping defined on a subset of a metric space, a normed linear space, a topological vector space or some suitable space.

Several problems can be modeled as equations of the form T x = x, where T is a given self-mapping defined on a subset of a metric space, a normed linear space, a topological vector space or some suitable space.

Several problems can be changed as equations of the form T x = x, where T is a given self-mapping defined on a subset of a metric space, a normed linear space, a topological vector space or some suitable space.

Let T be a self-mapping defined on C and satisfies one of the following: (i) T is a nonspreading mapping;   (ii) T is a hybrid mapping;   (iii) T is a TY mapping.  .