we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

urbanisation is still one of the social themes in developing countries. in china, the rapid process of urbanisation and economic growth bring to people not only more opportunities for creating new life and pursuing happiness, but also the challenge to face various and complex social, economical and environmental problems. among them some are outstanding, like the shrinking plowland devoured by ...

In this paper, we first give a new definition of Ω-Dedekind complete Riesz space (E,≤) in the frame vector metric (Ω,ρ,E) and investigate relation between Dedekind our concept. Moreover, introduce contraction so called α-vector proximal mapping. Then, prove certain best proximity point theorems for such mappings spaces where is space. Thus, time, acquire results on spaces. As result, generalize...

Let (X,1) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Let F : X ×X Ã X be a mixed monotone set valued mapping. We obtain sufficient conditions for the existence of a coupled fixed point of F.