Sentence examples for mappings 1 from inspiring English sources

In 2008, Suzuki [1] introduced a class of single valued mappings 1 2 ∥ x − T x ∥ ≤ ∥ x − y ∥ implies ∥ T x − T y ∥ ≤ ∥ x − y ∥ (C).

Furthermore, we prove that if T is replaced with the sequence of average mappings ( 1 − β n ) I + β n T ( n ≥ 0 ) such that 0 < β ∗ ≤ β n ≤ β ∗ < 1, where β ∗ and β ∗ are two positive constants, then the same result still holds provided conditions (i) and (ii) are satisfied.

To this end, we compose three well-known conformal mappings: 1. η = 1 ı ζ + 1 ζ - 1 Open image in new window maps the unit disk D Open image in new window conformally onto the upper half-plane H : = { η ∈ C : J η > 0 } Open image in new window.

Furthermore, we prove that if T is replaced with the sequence of average mappings ( 1 − β n ) I + β n T ( n ≥ 0 ) such that 0 < β ∗ ≤ β n ≤ β ∗ < 1, where β ∗ and β ∗ are two positive constants, then the same convergence result holds provided conditions (i) and (ii) are satisfied.

For all domains, we found that reviewers agreed about 93% of 1,717 possible mappings (101 items mapped by both reviewers multiplied by 17 domains).

As a balance between maximizing mapping success and minimizing multiple spurious mappings, 10 kb was chosen as the flanking region size (see supplementary materials, Supplementary Material online).

Recently, Akram et al. [12] introduced a new class of contraction maps, called A-contractions, which is a proper generalization of Kannan's mappings [9], Bianchini's mappings [13], and Reich type mappings [14].

Those include an interactive atlas of tomb mappings; 66 narrated tours; a 3-D exploration of one of the largest and most beautiful tombs, KV 14; and a searchable database of text and images.

In 1956 Beurling and Alhfors solved the boundary value problem for quasiconformal mappings [1].

Normal Mann iterative scheme is an important iterative scheme to study the class of nonexpansive mappings [1].

In 2012, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave fixed point results for such mappings [1].