| Abstract: |
| We study extensions of basic fixed-point theorems to semilinear operator equations. Using an approach that moves from concrete algorithms to abstract operator formulations, we establish a class of generalized existence and multiplicity results for fixed points on order intervals in partially ordered Banach spaces. The results are obtained under conditions that relax or replace the usual compactness and cone assumptions and are designed to accommodate semilinear operators arising in applications. In particular, the theorems recover and extend classical results and provide verifiable conditions for a broader class of nonlinear operators. |
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