As usual in the asymmetric information literature, we suppose the hypothesis that the (mathbb {F} -conditional law oF} -conditionalnt and hence admits a positive density with respect to its probabilawy law.
Suppose the hypothesis of η>0, after determination of K, using (12) and (14), CS would be eliminated by correction the estimation of symbol rate at the receiver, according to the following equation: hat{R}_{s}^{{new}} = left({1 - frac{1}{K}} right){hat R_{s}} (17).
Suppose the hypotheses of Theorem 1.1hold.
(Intrinsic (L^2) extension) Suppose the hypotheses of Theorem 5.20 are satisfied.
However, this approach supposes the asymmetry hypothesis hence, could not be used for others types of modalities.
Suppose the following hypotheses hold: (1) K : [0, T] × [0, T] × ℝ+ → ℝ+ and g : ℝ → ℝ are continuous.
We suppose the following hypotheses to hold: (i) T and R are continuous, (ii) (TXsubseteq RX), (iii) T is weakly increasing with respect to R, (iv) the pair ((T,R)) is compatible. .
holds for each ( x, y, z ) ∈ X × X × X. Suppose the following hypotheses: (1) T X ⊆ S X. (2) If S u ≠ T u, then inf { Ω ( S x, T x, S u ) : x ∈ X } > 0. .
Let (X, d) be a complete cone metric space with a solid cone P. Let T, f :X → X be mappings satisfying: d ( T x, T y ) ≽ a d ( f x, f y ). for all x, y ∈ X where a > 1. Suppose the following hypotheses: (1) fX ⊆ TX. (2) TX is a complete subspace of X. .
Let (X,d) be a cone metric space with a solid cone P. Let T, f : X → X be mappings satisfying: d ( T x, T y ) ≽ a d ( f x, f y ) + b d ( f x, T x ). for all x, y ∈ X where a, b ≥ 0 with a + b > 1 and b < 1. Suppose the following hypotheses: (1) fX ⊆ TX. (2) TX is a complete subspace of X. .
