Let be a Banach space with the dual space, and let be a proper subdifferentiable functional.
Let be a bifunction, let and be single-valued mappings, and let be a proper lower semicontinuous functional.
Let H be a real Hilbert space, (varphi H to R cup { + infty }) be a proper, convex, lower semicontinuous functional.
Let be a proper, convex, and lower semicontinuous functional.
Let C be a nonempty, closed, and convex subset of E. Let Λ be an index set, and f i : C → C be a proper, lower semicontinuous, and convex functionals, for every i ∈ Λ. Assume that ⋂ i ∈ Λ ( ∂ f i ) − 1 ( 0 ) is nonempty.
(ii) If,, (Hilbert space) and,, where is a proper, -subdifferentiable functional and denotes the -subdifferential operator of, then problem(3.3) changes to the problem associated with the following system of variational-like inequalities, which is finding such that (34) .
If,, (Hilbert space) and,, where is a proper, -subdifferentiable functional and denotes the -subdifferential operator of, then problem(3.3) changes to the problem associated with the following system of variational-like inequalities, which is finding such that (34).
In a separate beaker, calculated amount of a proper functional monomer was mixed with ethanol (3 mL) and ammonium fluoride (1.9 mL of 1 % aqueous solution), acting as a catalyst role.
