Abstract
The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.
Highlights
In [1,2], the notion of a b-metric space was initiated and some usual fixed point results have been provided
One of applications of contractive mappings was used for maximum likelihood estimation of the multiple linear regression parameters in the generalized Gauss–Laplace distribution assumption of the measurement’s errors [36]
For example a = b we get that for a = b ≥ 272, all the conditions of Theorem 1 are satisfied, i.e., Ω is a convex contraction of order 2 and has a unique fixed point
Summary
In [1,2], the notion of a b-metric space was initiated and some usual fixed point results have been provided. Many new results in this space were obtained over the past ten years (see for example [3,4,5,6]). Istratescu [7] considered convex contraction mappings in metric spaces and showed that each convex contraction mapping of order two admits a unique fixed point. The Istratescu’s result has recently caused the attention and was the object of examination in b-metric spaces (see [8]). Our paper is a generalization of the Istratescu’s result for convex contractions of order n in b-metric spaces (and in almost b-metric spaces and in quasi b-metric spaces)
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