Dislocated metric space differs from metric space for a property that self distance of a point needs not to be equal to zero. This property plays an important role to deal with the problems of various disciplines to obtain fixed point results. In this article, we establish a common fixed point theorem for two pairs of weakly compatible mappings which generalize and extend the result of Brain Fisher [1] in the setting of dislocated metric space with replacement of contractive constant by contractive modulus for which continuity of mappings is not necessary and compatible mappings by weakly compatible mappings.

This paper, gives an answer for the Question 1.1 posed by Hitzler (Generalized metrics and topology in logic programming semantics, 2001) by means of "Topological aspects of d-metric space with d-neighborhood system". We have investigated the topological aspects of a d-neighborhood system obtained from dislocated metric space (simply d-metric space) which has got useful applications in the semantic analysis of logic programming. Further more we have generalized the notion of F-contraction in the view of d-metric spaces and investigated the uniqueness of fixed point and coincidence point of such mappings.

In this paper, we prove some fixed point theorems using various cyclic contractions in weaker forms of generating spaces. MSC: 47H10; 54H25Keywords: generating space of b-dislocated quasi-metric family; generating space of b-quasi-metric family; generating space of quasi-metric family; generating space of b-dislocated metric family; generating space of dislocated quasi-metric family; generating space of dislocated metric family;

In this paper, we introduce the new classes of Hardy-Rogers type cyclic contractions and prove pertinent fixed point theorems for these Hardy-Rogers type contractions in the generating space of a b-dislocated metric family. MSC: 47H10; 54H25

Dislocated symmetric spaces are introduced, and implications and nonimplications among various kinds of convergence axioms are derived.