In this paper, we establish a fixed-point theorem for mixed monotone operators in ordered Banach algebras by introducing a novel contraction condition formulated in terms of the product law, which represents a significant departure from the traditional additive approach. By exploiting the underlying algebraic structure, our method ensures both the existence and uniqueness of fixed points under broader conditions. To illustrate the effectiveness of the proposed theorem, we also provide a concrete example that demonstrates its applicability.

We introduce a new methodological approach for the approximation of generalized offset surfaces using smoothing radial basis functions (RBFs). Existing offset surface generation methods often exhibit limitations such as self-intersections and singularities, which affect their robustness and accuracy. To address these issues, we employ generalized Wendland radial basis functions, which are compactly supported and provide enhanced stability. We establish the existence and uniqueness of the solution of the proposed method, analyze its computational aspects, and prove convergence results. Finally, numerical experiments are presented to demonstrate its effectiveness as well as to compare it with an existing method from the literature.