On Sums Over Partially Ordered Sets

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets

This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...

A solution of Volterra-Hamerstain integral equation in partially ordered sets

Witt rings of quadratically presentable fields

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...

Fixed point theorems for $alpha$-$psi$-contractive mappings in partially ordered sets and application to ordinary differential equations

‎In this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.