On set-valued fixed points, their geometry and solution of boundary value problem for a differential inclusion

We propose novel contractions to initiate set-valued fixed points and fixed figure conclusions, and validate these with illustrative examples to confirm the genuineness of the hypotheses. This ongoing work is driven by the geometric intricacies of set-valued fixed points, which play a pivotal role in addressing real-world challenges and making it captivating as well as innovative. These results contribute to the study of set-valued fixed points, their geometric properties, and their applications to boundary value problems involving differential inclusion and has considerable significance.