Abstract
In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the w t -distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness of the found fixed point.
Highlights
Introduction and PreliminariesThe concept of distance is one of the first concepts discovered by mankind
The distance notion has been discussed, refined and generalized in various ways. In this manuscript, we focus on b-metric and wt-distance
We have considered two new contractions in the setting of wt-distance over b-metric space
Summary
The concept of distance is one of the first concepts discovered by mankind. The concept of distance was first formulated by Euclid. A distance function δ forms a (standard) metric if δ(υ, ω ) ≤ δ(υ, ν) + δ(ν, ω ), for all υ, ν, ω ∈ X. As it is well known, the metric notion has been extended in several ways. Let d be a distance function on X = [0, ∞) that is defined as d (υ, ν) = |υ − ν| p , p > 1. Let μ be a non-decreasing auxiliary distance function so that for any t ∈ [0, ∞) we have lim μn (t) = 0. An auxiliary distance function Sb , formulated by Sb (t) = ∑ sk μk (t), t ∈ [0, ∞), is continuous at 0 and k =0 increasing. (4) if q (ν, υk ) ≤ ck for all k ∈ N, (υk ) is Cauchy sequence
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