d-Neighborhood system and generalized F-contraction in dislocated metric space

Abstract

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.

Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications

“…More particularly, the techniques used to obtain fixed points in [1] have attracted several authors. In this scenario, many authors imposed various restrictions to obtain the existence of a fixed point (see for example [10][11][12][13][14][15]).…”

Some Common Fixed Point Theorems Satisfying Meir-Keeler Type Contractive Conditions

“…Since then, many authors have established fixed point theorems in dislocated metric space. In the literature one can find many interesting recent articles in the field of dislocated metric space (See for examples [17] In this paper, we establish some common fixed point theorems for two pairs of compatible and weakly compatible mappings satisfying Meir-Keeler type contractive condition in dislocated metric space.…”

An Integral Type Common Fixed Point Theorem in Dislocated Metric Space

“…Since then, many authors have established fixed point theorems in dislocated metric space. In the literature one can find many interesting articles in the field of dislocated metric space(See for examples [6,7,8,9,11,12]). The study of fixed points of mappings satisfying a general contractive condition of integral type have been a very interesting and active field of research activity after the establishment of a theorem by A. Branciari [2].…”