Abstract
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. MSC:47H10, 54H25.
Highlights
Introduction and preliminaries TheBanach contraction principle is one of the simplest and most applicable results of metric fixed point theory
Sarma and Kumari [ ] established the existence of a topology induced by a dislocated metric which is metrizable with a family of sets {B(x, ε) ∪ {x} : x ∈ X, ε > } as a base, where B(x, ε) = {y ∈ X : dl(x, y) < ε} for all x ∈ X and ε >
We show that each b-dislocated metric space on X generates a topology τbd whose base is the family of open bd-balls
Summary
We give the definition of a b-dislocated metric space. A mapping bd : X × X → [ , ∞) is called a b-dislocated metric (or bd-metric) if the following conditions hold for any x, y, z ∈ X and s ≥ :. Let (X, dl) be a dislocated metric space, and bd(x, y) = (bl(x, y))p, where p > is a real number. Sarma and Kumari [ ] established the existence of a topology induced by a dislocated metric which is metrizable with a family of sets {B(x, ε) ∪ {x} : x ∈ X, ε > } as a base, where B(x, ε) = {y ∈ X : dl(x, y) < ε} for all x ∈ X and ε >. We show that each b-dislocated metric space on X generates a topology τbd whose base is the family of open bd-balls. For each positive integer i, there is αi ∈
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