An Analysis of Böhm's Theorem

Böhm's theorem for Berarducci trees

Böhm's Theorem for Resource Lambda Calculus through Taylor Expansion

We study the resource calculus, an extension of the λ-calculus allowing to model resource consumption. We achieve an internal separation result, in analogy with Böhm’s theorem of λ-calculus. We define an equivalence relation on the terms, which we prove to be the maximal non-trivial congruence on normalizable terms respecting β-reduction. It is significant that this equivalence extends the usua...

Böhm's Theorem, Church's Delta, Numeral Systems, and Ershov Morphisms

In this note we work with untyped lambda terms under β(η)-conversion and consider the possibility of extending Böhm’s theorem to infinite RE sets. Of course, it is well known that Böhm’s theorem will fail in general for such sets even if it holds for all finite subsets. It turns out that generalizing Böhm’s theorem to infinite sets involves three other superficially unrelated notions; namely, C...

On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

Generalization of Darbo's fixed point theorem and application

In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.