K. P. R. Rao

On the concepts of balls in a D-metric space

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.

On convergent sequences and fixed point theorems in D-metric spaces

Examples of complete D-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 complete D-metric space having a convergent sequence with infinitely many limits is given and, using the example, several fixed point theorems in D-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 the D-metric in any two variables and the theorems so obtained are illustrated by means of examples.

ON THE TOPOLOGY OF D-METRIC SPACES AND GENERATION OF D-METRIC SPACES FROM METRIC SPACES

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 T1 but not Hausdorff, and (2) an example of a D-metric space in which D-metric convergence defines a metrizable topology but the D-metric is not continuous even in a single variable.

COMMON STATIONARY POINTS FOR SET-VALUED MAPPINGS

Several theorems on stationary points for set-valued mappings have obtained. These are improvements upon some earlier results due to Fisher.

COMMON FIXED AND COINCIDENCE POINT THEOREMS FOR MAPS IN MENGER SPACE WITH HADZIC TYPE t - NORM

In this paper, we obtain a unique common fixed point theorem for two weakly compatible mappings in a Menger space and also obtain a common coincidence point theorem for two hybrid pairs of mappings.