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Open AccessArticle

On Almost b-Metric Spaces and Related Fixed Point Results

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Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
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Faculty for Traffic and Transport Engineering, University of Belgrade, 11000 Belgrade, Serbia
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School of Computing, Union University, 11000 Belgrade, Serbia
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Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
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China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 70; https://doi.org/10.3390/axioms8020070
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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