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Let f,T X→X be two mappings such that f(X)⊆T X), dominating map f is a weak annihilator of T. Suppose that for every three comparable elements x,y,z∈X, ψ G ( fx, fy, fz ) ≤ ψ M 4 ( x, y, z ) − φ M 4 ( x, y, z ), Open image in new window (59).
Let f,R,S,T X→X be four mappings such that f(X)⊆R(X)∪S X)∪T X) and dominating map f is a weak annihilator of R, S, and T. Suppose that for every three comparable elements x,y,z∈X, ψ G ( fx, fy, fz ) ≤ ψ M 1 ( x, y, z ) − φ M 1 ( x, y, z ), Open image in new window (56).
Thus f is a dominating map.
Thus g is dominated and f is a dominating map.
Since, T is dominating map, therefore Sx k ≤ TSx k.
Since x ≤ x n = T x for all x ∈ X, T is a dominating map.
Similar(31)
Let f,g,R,S X→X be four mappings such that f(X)⊆R(X) and g(X)⊆S X) and dominating maps f and g are weak annihilators of R and S, respectively.
Mapping is a big boy's game, with Google Maps, Bing Maps, and MapQuest dominating maps on both the Web and mobile.
Since dominating maps f and g are weak annihilator of T and S, respectively so for all n ≥ 1, and.
We assume the following hypotheses: (i) ( S, T ) is a.r. at some point x 0 ∈ X ; (ii) X is ( S, T ) -orbitally complete at x0; (iii) T and S are weakly increasing; (iv) T and S are dominating maps.
((mathcal G,F )) is asymptotically regular at some point (x_0in mathcal X ); (mathcal X ) is ((mathcal G,F ))-orbitally complete at (x_0); (mathcal F ) and (mathcal G ) are weakly increasing; (mathcal F ) and (mathcal G ) are dominating maps.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com