Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations
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MDPI
Materia
Banach algebras fixed point theory functional equations
Date
2022-11-09Referencia bibliográfica
Ben Amara, K; Berenguer, M.I.; Jeribi, A. Mathematics 2022, 10, 4179. [https://doi.org/10.3390/math10224179]
Sponsorship
University of Sfax (Tunisia); Junta de Andalucía (Spain), Project Convex and numerical analysis, reference FQM359, and by the María de Maeztu Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/ 501100011033/Abstract
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.