A Common Fixed Point Theorem for Two Pairs of Mappings in Dislocated Metric Space

Abstract

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.

Fixed point theorems in dislocated quasi-metric spaces

“…Zeyada et al [15] established the notion of dislocated quasi-metric spaces by generalizing the results of Hitzler and Seda [6]. Aage and Salunke [1,2], Isufati [7], Jha and Panthi [8], Jha et al [9], Panthi et al [10], Patel and Patel [11], Sarwar et al [13], Shrivastava et al [14], Zoto et al [16], and Zoto et al [17] gave some fixed point results in dislocated metric and dislocated quasi-metric spaces. Piri [12] obtained some Suzuki type fixed point theorems in complete cone b-metric spaces over a solid vector space.…”

A common fixed point theorem for Reich type co-cyclic contraction in dislocated quasi - metric paces

“…Some of the generalizations weaken the contractive nature of the map; for example see (Kannan, 1968;Kannan, 1969;Jungck, 1976;Sessa, 1982;Kirk et al, 2003;Karapinar and Erhan, 2011), and others. In other generalizations the ambient space is weakened; see (Zeyada et al, 2005;Aage and Saluke, 2008;Abbas et al, 2011;Chaipunya et al, 2012;Zoto et al, 2012;Panthi et al, 2015). This celebrated theorem can be stated as follows.…”

Fixed point theorems for contractive mappings and Ciric-Maiti-Pal orbit mappings of contractive type in re-defined generalized metric spaces

“…Subsequently, a lot more people do work around this kind of spaces [11]. Hitzler and Seda have focused fixed point theorems on dislocated metric spaces defined by themselves [10], more relevant results based on such spaces followed in recent years [21,28]. A lot of mathematicians [1,2,[13][14][15][16]27] have given fixed point results on modular spaces since Nakano [17] introduced the notion of modular spaces as a generalization of metric spaces in 1950.…”