Sentence examples for mappings was first from inspiring English sources

Remark 1.2 The class of relatively nonexpansive mappings was first considered in Butnariu et al. [3].

The class of κ-strictly pseudocontractive mappings was first introduced by Browder and Petryshyn [35] in Hilbert spaces.

The class of asymptotically κ-strictly pseudocontractive mappings was first introduced in Hilbert spaces by Qihou [3].

The class of k-strictly asymptotically pseudocontractive mappings was first introduced in Hilbert spaces by Qihou [3].

The existence of endpoints for a special kind of contractive mappings was first studied by Aubin and Siegel [1].

The class of (quasi- Bregman strongly nonexpansive mappings was first introduced in [21, 45] (for more details, see also [46]).

In fact, the asymptotically nonexpansive and asymptotically pseudocontractive mappings were first introduced by Goebel-Kirk [1] and Schu [2], respectively.

Scalar minimax theorems and set minimax theorems for non-continuous set-valued mappings were first proposed by Lin et al. [1].

Remark 1.2 The class of relatively asymptotically nonexpansive mappings were first considered in [4]; see also, [5] and the references therein.

The class of quasi-ϕ-nonexpansive mappings and the class of asymptotically quasi-ϕ-nonexpansive mappings were first considered in Zhou et al. [24] (see also Qin and Agarwal [18], Qin et al. [20], Qin et al. [21], Qin et al. [41]).

(I2) dually, for each v ∈ T ( y ) there is u ∈ T ( x ) such that u ⪯ v. Isotone mappings were first studied by Smithson [16], and it is well known that one of these conditions may be satisfied while the other is not.