Abstract
AbstractThe purpose of this paper is to establish some fixed point results for cyclic contractions in the setting of dislocated quasi-b-metric spaces. We verify that some previous cyclic contraction results in dislocated quasi-b-metric spaces are just equivalent to the non-cyclic ones in the same spaces. Moreover, by using two examples, we highlight the superiority of the results obtained.
Highlights
Introduction and preliminaries French mathematicianPoinćare was first to use the concept of fixed point in ‘Poinćare’s final theorem’ during the period of to, from restricting the existence of periodic solution for three body problem to the existence of fixed point under some conditions of planar continuous transformations
Due to its beautiful assertion and successful way of solving the implicit function existence theorem, the existence of a solution for a differential equation with initial value condition, fixed point theory caught the eyes of scholars and it sparkles people’s inspirations towards in-depth and extensive research
In recent decades, with the development of the computer, many people have coped with numerous applications by utilizing a variety of iteration methods to approach the fixed point and they made a breakthrough and brought this subject gradually to perfection
Summary
We could use the same method as in the proof of Theorem . We announce the result for the existence of fixed point under cyclical consideration in the framework following dislocated quasi-b-metric spaces. Proof Since (X, d) is dqb-complete, dqb-Cauchy sequence {Tnx} converges to some z ∈ X. P} and T(Ap+ ) ⊆ A , we conclude that {Tnx} has infinite terms in Ai for all i ∈. As Ai is closed for all i ∈ { , , . The following two examples support our Theorem .
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