Lipschitz implicit function theoremSemi-inner productBanach spaceThis paper presents several Lipschitz implicit function theorems for maps between Banach spaces. The results use semi-inner products as a means fo
Theorem 1 Let A, B be two nonempty subsets of a metric space (X,d) such that A is complete and A0 is nonempty. Assume that T:A→B is a continuous implicit relation type modified α3-proximal contraction such that the following conditions hold: (i) T is an α3-proximal admissible...
So, in view of Theorem 2.1, T has at least one fixed point lies in D¯. This shows there is at least one solution of the proposed system (1.1). □4 Stability results In this section, we will investigate the stability results in the sense of Ulam for the proposed system (1.1)....
(5.9) Applying the vec operator and Roth's theorem to both sides gives vec 0 = N−1 T ⊗ Is dvec N + (Is ⊗ N) dvec N−1 (5.10) Solving for dvec N gives dvec N = N−1 T ⊗ Is −1 (Is ⊗ N) dvec U (5.11) To simplify this, it helps to know two ...
We shall characterize, in Theorem VI.5.1, subjective expected utility ... P Wakker - Springer Netherlands 被引量: 339发表: 1989年 Stochastic dominance and the maximization of expected utility In attempting to construct a general framework for the analysis of choice under uncertainty, researchers ...
Binding functionDelta methodExact biasImplicit continuous mapsIndirect inferenceMaximum likelihoodThe delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods...
Our approach makes use of [14, Theorem 3.2] based on the pathwise calculus and allows us to obtain strong convergence with no limitations on T for a substantially larger class of noises. In fact, we require only Ho¨lder continuity of the noise and some moment condition on the ...
Maximizing the logarithmic function in the formula is equivalent to minimizing the loss function. The loss function is shown in Equation (8): 𝐿(𝑅,𝑤,𝑝,𝑞)=𝜆𝑝2‖𝑝‖2𝐹+𝜆𝑞2‖𝑞‖2𝐹+12∑𝑖=1𝑛∑𝑗=1𝑚𝐼𝑅𝑖𝑗(𝑅𝑖𝑗−𝑔(𝛼𝑝𝑖...