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 ...

‎In this paper we take $mathcal A$ to be the category {bf Pos-S}‎ ‎of $S$-posets‎, ‎for a posemigroup $S$‎, ${mathcal M}_{pd}$ to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ ‎$S$-...

Given a family of sets S, where the sets in S admit k ‘degrees of freedom’, we prove that not all (k + 1)-dimensional posets are containment posets of sets in S. Our results depend on the following enumerative result of independent interest: Let P (n, k) denote the number of partially ordered sets on n labeled elements of dimension k. We show that logP (n, k) ∼ nk log n where k is fixed and n i...

In this paper, we investigate the properties of various relations, operators and upper sets on partially ordered sets. Mathematics Subject Classification: 03E72, 54A40, 54B10

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

First, we establish a useful characterization of effective sets in conditionally complete partially ordered sets. Then, we prove that each maximal nonexpansive partial multiplier on a conditionally complete and infinitely distributive partially ordered set with upper bounded centre is inner. Finally, we show that some analogous results hold for T1-families of sets partially ordered by inclusion.