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Herein, a generalized Yosida inclusion problem involving Φ-relaxed co-accretive mapping is investigated. The resolvent and analogous generalized Yosida approximation operator is explicated and its characteristics are outlined. Picard S-type iterative algorithm is presented and convergence is delineated. Further, an equivalence of generalized Yosida inclusion problem to generalized resolvent equation problem is developed. Moreover, the convergence analysis of a contrived iterative scheme is reported to inspect the generalized resolvent equation problem. Finally, a delay differential equation is investigated and theoretical findings are exemplified.