Fall 2023 EXISTENCE, UNIQUENESS AND ABSTRACT APPROACH TO HYERS–ULAM STABILITY IN BANACH LATTICE ALGEBRAS AND AN APPLICATION
Nadir Benkaci-Ali
J. Integral Equations Applications 35(3): 259-276 (Fall 2023). DOI: 10.1216/jie.2023.35.259

Abstract

The abstract equation of the form u=KuL(Fu) is investigated in this paper. By applying a fixed point theorem for the product of operators K and A=L(F) defined on a Banach lattice algebra E, we obtain existence and uniqueness results of fixed points of the operator T=KA. Moreover, we state a sufficient condition on the spectral radius of a majorant linear mapping of L under which the equation u=Tu has the L-Hyers–Ulam stability. As an application, the obtained results are used to prove existence and uniqueness of solutions and Hyers–Ulam stability of a (p1,p2,,pn)-Laplacian hybrid fractional differential system. An example is also constructed to illustrate the main results. This work contains many new ideas, and gives a unified approach applicable to several types of differential and integral equations.

Citation

Download Citation

Nadir Benkaci-Ali. "EXISTENCE, UNIQUENESS AND ABSTRACT APPROACH TO HYERS–ULAM STABILITY IN BANACH LATTICE ALGEBRAS AND AN APPLICATION." J. Integral Equations Applications 35 (3) 259 - 276, Fall 2023. https://doi.org/10.1216/jie.2023.35.259

Information

Received: 7 July 2022; Revised: 1 February 2023; Accepted: 20 February 2023; Published: Fall 2023
First available in Project Euclid: 25 October 2023

Digital Object Identifier: 10.1216/jie.2023.35.259

Subjects:
Primary: 34B15 , 34B16 , 34B18

Keywords: abstract equation , fixed point , Hyers–Ulam stability

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.35 • No. 3 • Fall 2023
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