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 the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

Recently, Rahimi et al. [Comp. Appl. Math. 2013, In press] defined the concept of quadrupled fied point in K-metric spaces and proved several quadrupled fixed point theorems for solid cones on K-metric spaces. In this paper some quadrupled fixed point results for T-contraction on K-metric spaces without normality condition are proved. Obtained results extend and generalize well-known comparable...

The concept of partial metric which is a generalized metric space was introduced by Matthews 1 in 1994, inwhich the distance between two identical elements needs not be zero. The existence of fixed point for contraction-type mappings on such spaces was considered by many authors 1–12 . A modified version of a Banach contraction mapping principle, more suitable to solve certain problems arising ...

Following a recent paper of Zand and Nezhad [A generalization of partial metric spaces, Journal of Contemporary Applied Mathematics. 24 (2011) 86–93], we establish some fixed point results in GP -metric spaces. The presented theorems generalize and improve several existing results in the literature. Also, some examples are presented.

Binayak et al in [1] proved a fixed point of generalized Kannan type-mappings in generalized Menger spaces. In this paper we extend gen- eralized Kannan-type mappings in generalized fuzzy metric spaces. Then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. Finally we present an example of our main result.

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...

The purpose of this note is to give a natural approach to the extensions of the Banach Contraction Principle in metric spaces endowed with a partial order, a directed graph or a binary relation in terms of extended quasi-metric. This novel approach is new and may open the door to other new fixed point theorems. The case of multivalued mappings is also discussed and an analogue result to Nadler’...