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Mayor McKeon of West Orange, however, called a comparison with Livingston illogical, since it is a newer community and has more affluent residents.
A point p ¯ ∈ [ x ¯, y ¯ ] is called a comparison point for p ∈ [ x, y ] if d ( x, p ) = d M κ 2 ( x ¯, p ¯ ).
A point x ¯ ∈ [ q ¯, r ¯ ] is called a comparison point for x ∈ [ q, r ] if d M κ 2 ( q ¯, x ¯ ) = d ( q, x ).
A point z ¯ ∈ [ x ¯, y ¯ ] is called a comparison point of z ∈ [ x, y ] if d ( x, z ) = d M ( x ¯, z ¯ ).
A point p ¯ ∈ [ x ¯, y ¯ ] is called a comparison point for p ∈ [ x, y ] if ρ ( x, p ) = d M κ 2 ( x ¯, p ¯ ).
Any function ψ : R + → R + is called a comparison function if it satisfies the following properties: (1) ψ is monotonic increasing; (2) lim n → ∞ ψ n ( t ) = 0, t ≥ 0. .
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On Radio 4 yesterday morning, the Conservative MP Bernard Jenkin caught himself in the middle of what might today be called a "problematic" comparison, and put the engine swiftly into reverse.
Then φ is called a strong comparison function if the following assertions hold: (i) φ is increasing; (ii) φ n ( t ) → 0 as n → ∞ for all t ∈ R + ; (iii) ∑ n = 1 ∞ φ n ( t ) < ∞ for all t ∈ R +. .
A mapping (psi:[0,infty)to[0,isfty )) is called a b-comparison function if (i) ψ is monotone increasing; (ii) there exist (k_{0}inmathbb{N}), (ain 0,1)) and a convergent series of nonnegative terms (sum_{k=1}^{infty}v_{k}) such that b^{k+1}psi^{k+1}(t)leq a b^{k} psi^{k}(t)+v_{k} for (kgeq k_{0}) and any (tgeq0). .
Definition 5 [13] A function φ : ℝ+ → ℝ+ is called a (c -comparison func -comparisonatisfunction) φ if monotone itcreasatisfies) there exist k0 ∈ ℕ, a ∈ (0,1) and a convergent series of nonnegative terms ∑ k = 1 ∞ v k such that φ k + 1 ( t ) ≤ α φ k ( t ) + v k, for k ≥ k0 and any t ∈ ℝ+.
A map (A: Xrightarrow X) is called a β-ordered comparison map, if it is a comparison mapping and A(p oplus A q) leqbeta poplus q),quad mbox{for } 0 < beta< 1. [19].
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Justyna Jupowicz-Kozak
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