Fixed point theorems in b-metric spaces with applications to differential equations

Huang, Huaping; Deng, Guantie; Radenović, Stojan

doi:10.1007/s11784-018-0491-z

Cited by 28 publications

(10 citation statements)

References 15 publications

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“…In this manuscript, we aim to introduce the notion of a (b)-hybrid contraction that not only extends several existing contraction definitions but also merges a number of existing contractions. In particular, hybrid contractions aim to combine linear contractions [4][5][6][7][8][9][10][11] and nonlinear contractions [12][13][14][15][16][17] in the fixed point theory literature. After we investigate the existence of a fixed point for this new type contraction, we state some consequences.…”

Section: Introductionmentioning

confidence: 99%

New Hybrid Contractions on b-Metric Spaces

Karapınar

Fulga

2019

Mathematics

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Section: Introductionmentioning

confidence: 99%

New Hybrid Contractions on b-Metric Spaces

Karapınar

Fulga

2019

Mathematics

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“…Proving extensions of Banach contraction principle from metric spaces to b-metric spaces and hence to controlled metric type spaces is useful to prove existence and uniqueness theorem for different types of integral and differential equations. Some nice applications can be found for example in the recent article [22]. In fact, the authors in [17] gave a slightly modified application of a proven fixed point result.…”

Section: Introductionmentioning

confidence: 99%

Double Controlled Metric Type Spaces and Some Fixed Point Results

et al. 2018

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In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

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“…Theorem 4.1. (see [18]) Let (X, d) be a b-metric space with coefficient s ≥ 1. Let T : X → X be a mapping such that F(T ) = / 0 and…”

Section: The P-property Resultsmentioning

confidence: 99%

Some New Results in Partial Cone $b$-Metric Space

Kalkan

Şahin

2020

Communications in Advanced Mathematical Sciences

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In this paper, we introduce the concepts of the Ulam-Hyers-Rassias stability and the limit shadowing property of a fixed point problem and the P-property of a mapping in partial cone b-metric space. Also, we give such results by using the mapping which is studied by Fernandez et al. (Filomat 30(10) (2016)) in partial cone b-metric space and provide some numerical examples to support our results. The results presented here extend and improve some recent results announced in the current literature.

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Fixed point theorems in b-metric spaces with applications to differential equations

Cited by 28 publications

References 15 publications

New Hybrid Contractions on b-Metric Spaces

New Hybrid Contractions on b-Metric Spaces

Double Controlled Metric Type Spaces and Some Fixed Point Results

Some New Results in Partial Cone $b$-Metric Space

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