Rectangular b-metric space and contraction principles

Abstract

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

On some common coupled fixed point results in rectangular b-metric spaces

“…Note also that every b-metric space with coefficient s is a rectangular b-metric space with coefficient s 2 but the converse is not necessarily true ( [11,Example 2.7]). …”

“…In 2015, George et al [11] introduced the concept of rectangular b-metric space. It is well-known that rectangular b-metric space is an important generalization of usual metric space, b-metric spaces [7], and rectangular metric spaces.…”

Common tripled fixed point theorem in two rectangular b-metric spaces and applications

“…Recently, George et al [17] and Roshan et al [26] introduced the notion of rectangular b-metric space as follows: Definition 1.3 ([17, 26]). Let X be a nonempty set, s 1 be a given real number and let d : X × X → [0, ∞) be a mapping such that for all x, y ∈ X, the following conditions hold: Very recently, Ding et al [13,14] and Aydi et al [5] also discussed the fixed point and common fixed point problems of different contractive mapping for rectangular b-metric spaces.…”

Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces

“…the property that (X, d) is Haussdorf becomes superfluous. Moreover, from [8], [9], [22], we recall the definition of b-rectangular metric spaces (or b-generalized metric spaces), briefly b-g.m.s. Definition 1.2.…”

“…Finally, for the convenience of the reader, we recall some important results in brectangular metric spaces. In [9], George et.al.studied basic contraction-type mappings in b-rectangular metric spaces, like Kannan operators, i.e.…”