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Open AccessArticle

On Almost b-Metric Spaces and Related Fixed Point Results

Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
Faculty for Traffic and Transport Engineering, University of Belgrade, 11000 Belgrade, Serbia
School of Computing, Union University, 11000 Belgrade, Serbia
Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 70;
Received: 15 May 2019 / Revised: 22 May 2019 / Accepted: 23 May 2019 / Published: 1 June 2019
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
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. View Full-Text
Keywords: fixed point; Reich contraction; Hardy–Rogers contraction; almost b-metric space fixed point; Reich contraction; Hardy–Rogers contraction; almost b-metric space
MDPI and ACS Style

Mlaiki, N.; Kukić, K.; Gardašević-Filipović, M.; Aydi, H. On Almost b-Metric Spaces and Related Fixed Point Results. Axioms 2019, 8, 70.

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