Let (X, ) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X , then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F (x), F (y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈...

We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and coneto-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (...

in the present paper, we give a new approach to caristi's fixed pointtheorem on non-archimedean fuzzy metric spaces. for this we define anordinary metric $d$ using the non-archimedean fuzzy metric $m$ on a nonemptyset $x$ and we establish some relationship between $(x,d)$ and $(x,m,ast )$%. hence, we prove our result by considering the original caristi's fixedpoint theorem.

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...