On Almost <i>b</i>-Metric Spaces and Related Fixed Point Results

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.

Keywords

• fixed point
• Reich contraction
• Hardy–Rogers contraction
• almost <i>b</i>-metric space