Approximating fixed points of enriched contractions in Banach spaces

We introduce a large class of contractive mappings, called enriched contractions, a class which includes, amongst many other contractive type mappings, the Picard–Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed po...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 22; no. 2; p. 38
Main Authors: Berinde, Vasile, Păcurar, Mădălina
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2020
Springer Nature B.V
Subjects:
Analysis
Approximation
Banach spaces
Enrichment
Fixed points (mathematics)
Iterative methods
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Krasnoselskij iteration
Primary 47H05
fixed point
enriched contraction
Secondary 47H10
Banach space
54J25
strong convergence
Maia-type enriched contraction
local enriched contraction
ISSN:1661-7738, 1661-7746, 2730-5422
Online Access:Get full text
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Summary:We introduce a large class of contractive mappings, called enriched contractions, a class which includes, amongst many other contractive type mappings, the Picard–Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Krasnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results of this paper. We also study the fixed points of local enriched contractions, asymptotic enriched contractions and Maia-type enriched contractions. Examples to illustrate the generality of our new concepts and the corresponding fixed point theorems are also given.
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ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-020-0769-9