Sentence examples for proved related from inspiring English sources

They also proved related fixed point theorems.

Combining the four step scheme and the Euler Scheme, we defined a new numerical solution of the FBSDE system by branching particle systems in a random environment and proved related convergent results.

After this celebrated result[8], a number of authors have observed various other types of contraction mappings and proved related fixed point theorems (see e.g. such as Kannan [9], Reich [10], Hardy and Rogers [11], Ćirić [12 14], Zamfirescu [15], Arshad et al. [16]).

Some asymptotic properties of the distances between the sequences of domains and images of the sequences of non-self-mappings T n : A n → B n ; ∀ n ∈ Z 0 +, which converge uniformly to a limit non-self-mapping T : ⋃ j ∈ Z 0 + A 0 j → ⋃ j ∈ Z 0 + B 0 j, are given and proved related to the distance between the domain and image of the limit non-self-mapping.

Sixty-one spots showing differential expression and/or phosphorylation were analyzed by mass spectrometry and eighteen proteins were proved related to larval-pupal transformation.

However, the SFA say "the alleged breach was not proved" relating to disciplinary rule 77, which states that "a recognised football body, club, official, team official, other member of team staff, player, match official or other person under the jurisdiction of the Scottish FA shall, at all times, act in the best interests of Association Football".

We also prove related mean value theorems of Cauchy type.

In addition, we state and prove related theorems.

We also prove related results in the subjects of the irregularity of distribution, and approximation theory.

In this work, we introduce the concept of a cyclic compatible contraction and prove related fixed point theorems in the generating space of a b-quasi-metric family.

Analogously we can define shadowing property and stability of invertible time varying dynamical systems and prove related results for such systems which are proved for classical dynamical systems given by a homeomorphism.