ABOUT BOOK

Purpose A generalization of Ascoli–Arzelá theorem in Banach spaces is established. Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order. The authors’ results are obtained under, rather, general assumptions. Design/methodology/approach First, a generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. Second, this new generalization with Schauder's fixed point theorem to prove the existence of a solution for a boundary value problem of higher order is used. Finally, an illustrated example is given. Findings There is no funding. Originality/value In this work, a new generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. To the best of the authors’ knowledge, Ascoli–Arzelá theorem is given only in Banach spaces of continuous functions. In the second part, this new generalization with Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order, where the derivatives appear in the non-linear terms.