<p>This research considers a class of semilinear integrodifferential equations with state-dependent nonlocal conditions on a semi-infinite interval in Banach spaces. These equations involve nonlinear terms that depend on implicit spatial derivatives of the state variable. The global existence of solutions is first established through the use of fractional power operators, resolvent operator theory, Kuratowski measures of noncompactness, and fixed-point theory. In particular, the compactness of the resolvent operator is not required. It is further demonstrated that the solution set is compact. Additionally, under certain assumptions, the existence of quasi-invariant and globally attracting sets of solutions is investigated. Finally, an example is presented to demonstrate the applicability of the main results.</p>