Abstract
In this paper, first we describe the notion of dislocated Sb-metric space and then we introduce the new notions of generalized F-contraction and generalized F-Suzuki-contraction in the setup of dislocated Sb-metric spaces. We establish some fixed point theorems involving these contractions in complete dislocated Sb-metric spaces. We also furnish some examples to verify the effectiveness and applicability of our results.
Highlights
Introduction and PreliminariesBakhtin [1] and Czerwik [2] introduced b-metric spaces and proved the contraction principle in this framework
First we describe the notion of dislocated Sb-metric space and we introduce the new notions of generalized F -contraction and generalized F -Suzuki-contraction in the setup of dislocated Sb-metric spaces
In 2012, Sedghi et al [11] introduced the concept of S-metric space by modifying D-metric and G-metric spaces and proved some fixed point theorems for a self-mapping on a complete S-metric space
Summary
Bakhtin [1] and Czerwik [2] introduced b-metric spaces and proved the contraction principle in this framework. Piri and Kumam [6] extended the fixed point results of [12] by introducing a generalized F -Suzuki-contraction in b-metric spaces. [6] Let (X, d) be a complete b-metric space and T : X → X be a generalized F -Suzukicontraction. T has a unique fixed point x∗ ∈ X and for every x ∈ X the sequence {T nx} converges to x∗. We first introduce the concept of dislocated Sb-metric space and we demonstrate some fixed point results for generalized F -contractions and generalized F -Suzuki-contractions in such spaces. Let X = R+, the mapping Sb : X3 → R+ defined by Sb(x, y, z) = x + y + 4z is a complete dislocated Sb-metric on X with b = 2 It is not a dislocated S-metric space.
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