Existence and Unique Coupled Solution in Sb-Metric Spaces by Rational Contraction with Application

Vujaković, Jelena; Kishore, G.N.V.; Rao, K. P. R.; Radenović, Stojan; Sadik, Shaik

doi:10.3390/math7040313

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2019

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“…After, partial b-metric spaces [6], metric-like spaces [7] and b-dislocated metric spaces [8] have been given. For related contraction principles in the setting of above spaces, the readers can see [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On Almost b-Metric Spaces and Related Fixed Point Results

Mlaiki

Kukić

Gardašević-Filipović

et al. 2019

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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.

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