In this paperwe consider a linear scalar differential equationwith variable delays andgive conditions to ensure that the zero solution is asymptotically stable bymeans of fixedpoint theory.These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. 2...

We incorporate externalities into the stable matching theory of two-sided markets: We establish the existence of stable matchings provided that externalities are positive and agents’ choices satisfy substitutability, and we show that the standard insights of matching theory, such as the existence of side optimal stable matchings and the rural hospitals theorem, remain valid despite the presence...

In this paper we define a new type of fixedpoint of recursive definitions and investigate some of its properties. This opt imal fixedpoint (which always uniquely exists) contains, in some sense, the maximal amount of “interesting” information which can be extracted from the recursive definition, and it may be strictly more defined than the program’s least fixedpoint. This fixedpoint can be the ...

We consider an explicit iterate-to-fixedpoint operator and derive associated rules for both forward and reverse mode algorithmic differentiation. Like other AD transformation rules, these are exact and efficient. In this case, they generate code which itself invokes the iterate-to-fixedpoint operator. Loops which iterate until a variable changes less than some tolerance should be regarded as ap...

We generalize Abrahamse’s interpolation theorem from the setting of a multiply connected domain to that of a more general Riemann surface. Our main result provides the scalar-valued interpolation theorem for the fixedpoint subalgebra of H∞ associated to the action of a Fuchsian group. We rely on two results from a paper of Forelli. This allows us to prove the interpolation result using duality ...

Tree basis in Banachs spaces, which are Schauder basis spaces with nice “tree projections”, which is a property strictly between conditional and unconditional basis, are classified. Stronger basis properties like symmetric, and subsymmetric have weaker tree versions as well. These bases are motivated by well known adaptive approximation algoritms.

We introduce a general iterative algorithm for finding a common element of the common fixedpoint set of an infinite family of λi-strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the prop...

In this paper, we devote to investigation of the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations { D0+u(t)+ f (t,u(t)) = 0, 0 < t < 1, u(0) = u′(0) = · · ·u(n−2)(0) = D0+u(1), where D0+ , D β 0+ are the standard Riemann-Liouville fractional derivative, n− 1 < α n , n−2 β n−1 , n 3 . By means of constructing an exact cone of the Banac...

When a digital filter is realized with floating-point or fixed-point arithmetics, errors and constraints due to finite word length are unavoidable. In this paper, we show how these errors can be mechanically analysed using the HOL theorem prover. We first model the ideal real filter specification and the corresponding floating-point and fixedpoint implementations as predicates in higher-order l...