Fernandes de Oliveira, Luis AntonioArbach, Roseli2024-07-122024-07-122009Fernandes de Oliveira, L. A. ve Arbach, R. (2009). The subdifferential of a convex functional on regulated function space. Maltepe Üniversitesi. s. 234.9.78605E+12https://hdl.handle.net/20.500.12415/2256We treat here about the utilization of classic tools of Convex Analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b], X) of the regulated functions in [a, b], that is, the functions f : [a, b] ? X, X a Banach space, that have only discontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we report the initial investigation of the subdifferentiability of the lower-semicontinuous convex functional L?,f (x) of Nemytskii type, we had already introduced. This notion is related with the properties of directional derivative and with the notion of Gateaux differentiability. Then natural the investigation of its subgradients and the duality aspects, because the classical result on characterization of its global minimum in x0 by the condition 0 ? ?L?,f (x0).enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessConference Object235234