Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications

Abstract

We first introduce a new concept of b-dislocated metric space as a generalization of dislocated metric space and analyze different properties of such spaces. A fundamental result for the convergence of sequences in b-dislocated metric spaces is established and is employed to prove some common fixed point results for four mappings satisfying the generalized weak contractive condition in partially ordered b-dislocated metric spaces. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

Common fixed point results of generalized almost rational contraction mappings with an application

“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”

A note on fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces

“…Afterwards, many authors obtained numerous interesting results in ordered metric spaces as well as in ordered b-metric spaces (see [1,6,10,14,16]). …”

Fixed points of generalized (psi, s, alpha)-contractive mappings in dislocated and b-dislocated metric spaces

“…Recently, Hussain et al [3] introduced the notion of b-dislocated metric spaces. Some topological properties of dislocated and b-dislocated metrics were investigated in [3].…”

“…Recently, Hussain et al [3] introduced the notion of b-dislocated metric spaces. Some topological properties of dislocated and b-dislocated metrics were investigated in [3]. Very recently, many results on fixed points, coincidence points and common fixed points of mappings which satisfy certain contractive conditions in dislocated metric spaces where obtained, see [13]- [19] and references therein.…”

“…In 1989, Bakhtin [1] (and also Czerwik [2]) introduced the concept of bmetric spaces and presented contraction mappings in b-metric spaces that is a generalization of Banach contraction principle in metric spaces. For fixed point theory in b-metric spaces, see [3]- [11] and the references therein. In 2000, Hitzlerand and Seda [12] introduced the notion of dislocated metric spaces, in which the self distance of a point need not be equal to zero.…”