Some fixed point theorems in extended b-metric spaces

Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete metric spaces in 1922 by Banach. According to this principle, ”let (X, d) be a complete metric space...

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Bibliographic Details
Main Authors: Ozturk, Vildan, Turkoglu, Duran, Ansari, Arslan H.
Format: Conference Proceeding
Language:English
Subjects:
Fixed points (mathematics)
Metric space
Principles
Theorems
Online Access:Get full text
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Summary:Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete metric spaces in 1922 by Banach. According to this principle, ”let (X, d) be a complete metric space and f : X → X be a mapping. If there exists a constant 0 ≤ k < 1 such that for all x, y ∈ X, d( f x, f y) ≤ k.d(x, y), then f has a unique fixed point”. In this work, we define almost contraction in extended b-metric space and prove some fixed point theorems for mappings satisfying this type contraction.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0118603