<p>This paper addresses the split feasibility problem with multiple output sets in Hilbert spaces, wherein the feasibility sets are represented as sublevel sets of convex functions. In contrast to existing relaxed projection algorithms wherein half-spaces are constructed in distinct Hilbert spaces, the proposed approach constructs all half-spaces uniformly within a single Hilbert space. Based upon this conceptual framework, several relaxed projection algorithms are developed. Under standard conditions, the convergence of these algorithms is rigorously established. Numerical experiments demonstrate the effectiveness of the proposed algorithms and provide comparisons with existing relaxed projection methods.</p>