Benkaci-Ali, Nadir2024-03-142024-03-14202308973962https://projecteuclid.org/journals/journal-of-integral-equations-and-applications/volume-35/issue-3/EXISTENCE-UNIQUENESS-AND-ABSTRACT-APPROACH-TO-HYERSULAM-STABILITY-IN-BANACH/10.1216/jie.2023.35.259.short10.1216/jie.2023.35.259https://dspace.univ-boumerdes.dz/handle/123456789/13699The abstract equation of the form u = Ku · L(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 = K · A. Moreover, we state a sufficient condition on the spectral radius of a majorant linear mapping of L under which the equation u = T u 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.enAbstract equationFixed pointHyers–Ulam stabilityArticle