Sentence examples for mappings to a from inspiring English sources

(2) For the mappings, we extend the mapping from two quasi-nonexpansive mappings to a countable family of Bregman totally quasi-D-asymptotically nonexpansive mappings.

Wangkeeree et al. [16] established the continuity of the efficient solution mappings to a parametric generalized strong vector equilibrium problem involving a set-valued mapping under the Holder relation assumption.

In this paper, we introduce g-approximative multivalued mappings to a partial metric space.

It is worth mentioning that our main theorem generalizes recent theorems by Su et al. [12] from relatively nonexpansive mappings to a more general concept.

The following result improves the so-called viscosity approximation method which was first introduced by Moudafi [36] from nonexpansive mappings to a semigroup of pseudo-contractive mappings.

Moreover, Corollary 3.8 improves and extends Theorem MT of Matsushita and Takahashi [16] and Theorem 3.4 of Nilsrakoo and Saejung [36] from a relatively nonexpansive mappings to a finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings.

For the mappings, we extend the mappings from firmly quasi-nonexpansive mappings to an infinite family of one-to-one quasi-nonexpansive mappings.

Corollary 3.7 extends Theorem 3.1 of Zegeye and Shahzad [18] from a finite family of asymptotically nonexpansive mappings to an infinite family of asymptotically nonexpansive mappings.

Corollary 3.5 extends Theorem 3.1 of Inchan and Plubtieng [16] from two asymptotically nonexpansive mappings to an infinite family of asymptotically nonexpansive mappings.

Remark 3.4 Theorem 3.3 extends and improves the main results in Moudafi et al. [11 13] in the following aspects: (a) For the mappings, we extend the mappings from firmly quasi-nonexpansive mappings to an infinite family of one-to-one quasi-nonexpansive mappings.

Remark 3.2 Theorem 3.1 mainly improves Theorem 2.1 of Qin et al. [29] in the following aspects: (1) improves the mappings from a finite family of mappings to an infinite family of mappings;   (2) extends the framework of the space from a uniformly smooth and uniformly convex space to a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property.  .