Sentence examples for proximal nonexpansive from inspiring English sources

The existence of the best proximity point for the proximal nonexpansive mapping on starshaped sets is studied.

In this paper we focus on the sufficient conditions to ensure the existence of the proximity point for the proximal nonexpansive mapping.

There are two proximity point theorems for the proximal nonexpansive mapping, proved in [11].

T is a proximal nonexpansive.

T is continuous affine proximal nonexpansive.

That is, T is a proximal nonexpansive mapping.

Recently a new notion of the proximal generalized nonexpansive mapping was introduced in [20], and a few results about the proximity point for this class of mappings are given.

Eldred et al. [9] established the existence of best proximity points for cyclic relatively nonexpansive mappings by using a geometric notion of proximal normal structure in the setting of Banach spaces.

Eldred et al. [5] showed that every relatively nonexpansive mapping has a proximal point under certain conditions.

Note that the proximal mapping of g is firmly nonexpansive, namely, langle operatorname{prox}_{lambda g}x-operatorname{prox}_{lambda g}y,x-yrangle ge| operatorname{prox}_{lambda g}x-operatorname{prox}_{lambda g}y|^{2} for all (x,yin H_{2}) and it is also the case for the complement (I-operatorname{prox}_{lambda g}).

Let (T Arightarrow B) be continuous, proximally monotone, and proximal fuzzy ordered η-contraction such that, for any (t>0), (A_{0}(t) ) and (B_{0}(t)) are nonempty with (T(A_{0}(t))subseteq B_{0}(t)), (g Arightarrow A) surjective, fuzzy nonexpansive and inverse monotone mapping with (A_{0}(t)subseteq g(A_{0}(t))) for any (t>0).