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Mathematics > Functional Analysis

Title: Approximating fixed points of enriched contractions in Banach spaces

Abstract: We introduce a large class of mappings, called enriched contractions, 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 Kransnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results in 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.
Subjects: Functional Analysis (math.FA)
MSC classes: 47H09, 47H10
Cite as: arXiv:1909.02382 [math.FA]
  (or arXiv:1909.02382v1 [math.FA] for this version)

Submission history

From: Vasile Berinde [view email]
[v1] Thu, 5 Sep 2019 13:14:23 GMT (8kb)

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