<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we study the following problems: I. Let (<italic>M, d</italic>) be a complete metric space and <italic>f, g</italic> : <italic>M</italic> → <italic>M</italic> be two operators. We suppose that:(a) <italic>f</italic> is a Picard operator with its unique fixed point <italic>x *f</italic>;(b) there exists <italic>η ></italic> 0 such that <italic>d</italic>(<italic>f</italic>(<italic>x</italic>), <italic>g</italic>(<italic>x</italic>)) ≤ <italic>η</italic>, for every <italic>x</italic> ∈ <italic>M</italic>.The problem consists in estimating <italic>d</italic>(<italic>g</italic><italic>n</italic>(<italic>x</italic>), <italic>x</italic><italic>*</italic><italic>f</italic>), for <italic>x</italic> ∈ <italic>M</italic> and <italic>n</italic> ∈ 𝕅*.II. Let <italic>B</italic> be a Banach space and <italic>f, g</italic> : <italic>B</italic> → <italic>B</italic> be two operators. We suppose that <italic>f</italic> is a Picard operator. The problem is to find sufficient conditions which guarantee that <italic>f</italic> + <italic>g</italic> is a Picard operator.</abstract>

In this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:(a) f is a Picard operator with its unique fixed point x *f;(b) there exists η > 0 such that d(f(x), g(x)) ≤ η, for every x ∈ M.The problem consists in estimating d(gn(x), x*f), for x ∈ M and n ∈ 𝕅*.II. Let B be a Banach space and f, g : B → B be two operators. We suppose that f is a Picard operator. The problem is to find sufficient conditions which guarantee that f + g is a Picard operator.

Stability of Picard operators under operator perturbations

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Stability of Picard operators under operator perturbations"}

In this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:(a) f is a Picard...

Stability of Picard operators under operator perturbations

Published Online: Apr 30, 2020

Page range: 3 - 12

DOI: https://doi.org/10.2478/awutm-2018-0012

Keywords
metric spaces, fixed point, Picard operator, operator perturbation, data dependence of the fixed point

© 2018 Adrian Petruşel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Stability of Picard operators under operator perturbations

Published Online: Apr 30, 2020

Page range: 3 - 12

DOI: https://doi.org/10.2478/awutm-2018-0012

Keywordsmetric spaces, fixed point, Picard operator, operator perturbation, data dependence of the fixed point

© 2018 Adrian Petruşel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
metric spaces, fixed point, Picard operator, operator perturbation, data dependence of the fixed point