Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations

Making use of the Boyd-Wong fixed point theorem, we establish a new existence and uniqueness result and an approximation process of the fixed point for the product of two nonlinear operators in Banach algebras. This provides an adequate tool for deriving the existence and uniqueness of solutions of...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 22; p. 4179
Main Authors Ben Amara, Khaled, Berenguer, Maria Isabel, Jeribi, Aref
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2022
Subjects
Algebra
Approximation
Approximation theory
Banach algebras
Banach spaces
Control theory
Existence theorems
Fixed point theory
Fixed points (mathematics)
Functional equations
Mathematical research
Methods
Operator theory
Operators
Physics
Schauder bases
Uniqueness
Spain
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Summary:Making use of the Boyd-Wong fixed point theorem, we establish a new existence and uniqueness result and an approximation process of the fixed point for the product of two nonlinear operators in Banach algebras. This provides an adequate tool for deriving the existence and uniqueness of solutions of two interesting type of nonlinear functional equations in Banach algebras, as well as for developing an approximation method of their solutions. In addition, to illustrate the applicability of our results we give some numerical examples.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10224179