Introduction: Orlicz and Birnbaum considered spaces of functions with growth properties different from the power type growth control, provided by the p L -norm. This generalization found many applications in differential and integral equations with kernels of non-power types. A more abstract approach was given by Nakano in connection with the theory of order spaces. His point of view was genera...

For a class of operator inclusions with multivalued terms fulllling mixed semicontinuity hypotheses, the existence of solutions is established by chieey using Bressan and Colombo's directionally continuous selection theorem as well as Ky Fan's xed point principle. An application to the Cauchy problem is then performed.

We describe an encoding of major parts of domain theory and xed-point theory in the Pvs extension of the simply-typed-calculus; these formaliza-tions comprise the encoding of mathematical structures like complete partial orders (domains), domain constructions, the Knaster-Tarski xed-point theorem for mono-tonic functions, and variations of xed-point induction. Altogether, these encodings form a...

Convergence of a family of Markov jump processes evolving according to coagulation-fragmentation dynamics to the corresponding determin-istic equations is proved on every nite interval of existence. After obtaining local existence by the Banach xed-point theorem, we can prove global existence using the positivity of the limit function on the local existence interval.

An operational and a denotational semantic model are presented for a real-time programming language incorporating the concept of integration. This concept of integration, which has been introduced by Baeten and Bergstra 4], enables us to specify a restricted form of unbounded non-determinism. For example, the execution of an action at an arbitrary moment in a time interval can be speciied using...

In this paper, a box approximation scheme is proposed using the lumped mass numerical integration technique on piecewise linear nite element spaces for a coupled nonlinear thermistor system. Existence and uniqueness of the proposed box approximation scheme are proved via a xed point theorem, and H 1-error analysis is presented.

An operational and a denotational semantic model are presented for a real-time programming language incorporating the concept of integration. This concept of integration, which has been introduced by Baeten and Bergstra 4], enables us to specify a restricted form of unbounded non-determinism. For example, the execution of an action at an arbitrary moment in a time interval can be speciied using...

We provide suucient conditions for the convergence of Steeensen's method to a locally unique solution of a nonlinear operator equation on a Banach space. We use a xed point theorem and a special choice of divided diierences. Some applications of our results are also provided.

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fixed point theorems.

The Structural Induction Theorem (Lehmann and Smyth, 1981; Plotkin, 1981) characterizes initial F-algebras of locally continuous functors F on the category of cpo's with strict and continuous maps. Here a dual of that theorem is presented, giving a number of equivalent characterizations of nal coalgebras of such functors. In particular, nal coalgebras are order strongly-extensional (sometimes c...