for all x, y Î X, where : R+ ® R+ is a nondecreasing function such that lim n→∞ φ n(t) = 0 for all t > 0. In 1994, Matthews [4] introduced the notion of a partial metric space and obtained a generalization of Banach’s fixed point theorem for partial metric spaces. Recently, Altun et al. [5] (see also Altun and Sadarangani [6]) gave some generalized versions of the fixed point theorem of Matthew...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

in this paper, we prove a fixed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. the theorems presented are generalizations of very recent fixed point theorems due to abdeljawad, karapinar and tas. to emphasize the very general nature of these results, we illustrate an example.

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In the present paper, a partial order on a non- Archimedean fuzzymetric space under the  Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

This paper discusses balls in partial b-metric spaces and cone metric spaces, respectively. Let (X ,pb) be a partial b-metric space in the sense of Mustafa et al. For the family of all pb-open balls in (X ,pb), this paper proves that there are x, y ∈ B ∈ such that B′ B for all B′ ∈ , where B and B′ are with centers x and y, respectively. This result shows that is not a base of any topology on X...

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

By a metric-like space, as a generalization of a partial metric space, we mean a pair (X ,σ ), where X is a nonempty set and σ : X × X →R satisfies all of the conditions of a metric except that σ (x, x) may be positive for x ∈ X . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our resul...

In this paper we introduce the notion of quasi-partial b-metric space and then study coupled fixed point results in a quasi-partial b-metric space. Some examples are also given in support of the obtained results. Mathematics Subject Classification: 47H10, 54H25

Some new fixed point theorems for multi-valued operator satisfying increasing properties are proved in partial ordered metric space and in partial ordered Banach space, respectively.