An example of a D-metric space is given, in which D-metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D-metric spaces from a given metric space are developed and are used in constructing (1) an example of a D-metric space in which D-metric convergence defines a topology which is T 1 but not Hausdorff, and (2) [1,2,3,4,5,6,7,8,9,10,11,12,13,14]) have taken these claims for granted and used them in proving fixed point theorems in D-metric spaces.In this paper, we give examples to show that in a D-metric space (1) D-metric convergence does not always define a topology, (2) even when D-metric convergence defines a topology, it need not be Hausdorff, (3) even when D-metric convergence defines a metrizable topology, the D-metric need not be continuous even in a single variable. In fact, we develop certain methods for constructing D-metric spaces from a given metric space and obtain from them, as by-products, examples illustrating the last two assertions. We also introduce the notions of strong convergence, and very strong convergence in a D-metric space and study in a decisive way the mutual implications among the three notions of convergence, strong convergence, and very strong convergence.Throughout this paper, R denotes the set of all real numbers, R + the set of all non-

The various concepts of open balls in D-metric spaces are studied in the case of certain D-metric spaces and many results in the literature on such balls are shown to be false.

Examples of completeD-metric spaces are given in which every convergent sequence has at most two limits and in which there are convergent sequences with exactly two limits. Also an example of a completeD-metric space having a convergent sequence with infinitely many limits is given and, using the example, several fixed point theorems inD-metric spaces are shown to be false. Modifications of some of these theorems and their generalizations are obtained either by imposing restrictions on the number of limits of certain convergent sequences in the space or by assuming the sequential continuity of theD-metric in any two variables and the theorems so obtained are illustrated by means of examples.

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Abstract. In this paper, we extend and generalize Presic Type theorems for a pair of maps and Jungck type maps.

In this paper, we obtain a unique coupled common fixed point theorem for four maps in partial metric spaces. RESUMEN En este artículo obtenemos un teorema del punto fijo clásico acopladoúnico para cuatro aplicaciones en espacios métricos parciales.

We prove a related fixed point Theorem for four mappings which are not continuous in four fuzzy metric spaces, one of them is a sequentially compact fuzzy metric space. Our Theorem in the metric version generalizes Theorem 4 of [1]. Finally, We give a fuzzy version of Theorem 3 of [1].

We obtain a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Our result extends the recent results of B. Samet and C. Vetro (2011). We also introduced a suitable example supporting our result.