Fixed-Point Theorem with a Novel Contraction Approach in Banach Algebras

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.