Fixed points and lines in 2-metric spaces

Abstract

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.

Unique Common Fixed Points for Mappings Satisfying φ-Contractions on b2 Metric Spaces

“…As is known to all, the notion of metric spaces has been generalized by many scholars, of which the most essential work is the 2-metric spaces. In 1963, the notion of 2-metric spaces was first introduced by Gähler in [1], from then on, many scholars had proved the common fixed points theorems in this spaces [1] [2] [3]. In 1993, Czerwik introduced the notion of b-metric spaces [4], and proved theorems of common fixed points in this space.…”

A fixed point theorem for (μ, ψ)-generalized ƒ-weakly contractive mappings in partially ordered 2-metric spaces

“…(3). By choosing ψ(a, b) = a + b 2 for all a, b ≥ 0 and µ(t) = t for all t ≥ 0, we conclude that condition (1) holds. This prove that T is a (µ, ψ)-generalized f -weakly contractive mapping on the 2-metric space (X, d).…”

“…In addition, the fixed point theorems on 2-metric spaces and metric spaces may be unrelated easily [10]. There are many fixed point results on 2-metric spaces were stated and generalized, the readers may refer to [1,8,9,11,13,17,18,19] and references therein.…”

Tripled random coincidence point and common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

“…Finding the fixed point of contractive mapping becomes the center of strong research activity [3,9,10,24,32,37]. Recently, Huang and Zhang [18] and Bakhtin [8] introduced cone metric space and b-metric space, respectively, as some generalizations of usual metric spaces.…”