Abstract
In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b-metrics to the corresponding b-metrics. Later, we show that this approach can not work for all kinds of contractions. To confirm this, we present a proof in which the contraction condition is such that it cannot be reduced to corresponding b-metrics.
Highlights
In [1] Filipović and Kukić considered some classical contraction principles of Kannan [2], Reich [3]and Hardy–Rogers [4] in b-metric spaces and rectangular b-metric spaces without the assumption of continuity of the corresponding metric
As an attempt to continue in that spirit, we initiate the concept of almost b-metric spaces
The motivation of this initiation comes from [20] where Mitrović, George and Hussain introduced almost rectangular b-metric spaces
Summary
Nabil Mlaiki 1 , Katarina Kukić 2 , Milanka Gardašević-Filipović 3 and Hassen Aydi 4,5 *.
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