Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion , 2. topology, and 3. powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary m...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...

In the paper [9] we introduced the class of generalized metric spaces. These spaces simultaneously generalize ‘standard’ metric spaces, probabilistic metric spaces and fuzzy metric spaces. We show that every generalized metric space is, naturally, a uniform space. Thus we can use standard topological techniques to study, for example, probabilistic metric spaces. We illustrate this by proving a ...

In this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.  

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

In this paper, tripled coincidence points of mappings satisfying  $psi$-contractive conditions in the framework of partially ordered $G_b$-metric spaces are obtained. Our results extend the results of Aydi et al. [H. Aydi, E. Karapinar and W. Shatanawi, Tripled fixed point results in generalized metric space, J. Applied Math., Volume 2012, Article ID 314279, 10 pages]. Moreover, some examples o...

the aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. our results present random versions and extensions of some well-known results in the current literature.