On generalized Yosida inclusion problem with application

Abstract

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.

Keywords

• Yosida inclusion
• Resolvent operator
• Yosida approximation operator
• Resolvent equation
• Delay differential equation