(1) If we take g = [I.sub.x] as the

identity mapping on X, then we obtain the definition of [mathematical expression not reproducible] contractive mapping as in [28].

As observed above, logical induction is just an

identity mapping on an inductively idempotent logical identity--operator.

For each i [member of] {1, 2}, let [mathematical expression not reproducible] be a nonempty, closed, and convex set-valued mapping, and let [g.sub.i] : [H.sub.i] [right arrow] [H.sub.i] be [[alpha].sub.i]-Lipschitz continuous such that ([g.sub.i] - [I.sub.i]) is [[sigma].sub.i]-strongly monotone, where [I.sub.i] is the identity mapping on Hi.

For each i [member of] {1,2}, let [mathematical expression not reproducible] be a nonempty, closed, and convex set-valued mapping, and let [g.sub.i] : [H.sub.i] [right arrow] [H.sub.i] be [[delta].sub.i]-Lipschitz continuous such that ([g.sub.i] - I[.sub.i]) is [[sigma].sub.i]-strongly monotone, where [I.sub.i] is the identity mapping on [H.sub.i].

Let R : H [right arrow] H be [eta]-relaxed Lipschitz continuous mapping with constant a and I : H [right arrow] H be an identity mapping. Let [phi] : H [right arrow] R [union] {+[infinity]} be a lower semicontinuous, [eta]-subdifferential, proper functional which may not be convex and for any z,x [member of] H, the mapping h(y, x) = (z - (I - R)x, [eta](y, x)} is 0-DQCV in y.

Let P, R, f, g : H [right arrow] H, N, n : H x H [right arrow] H be the single-valued mappings such that g(H) = H, A, B, C, D : H [right arrow] CB(H) be the set-valued mappings, and I : H [right arrow] H be an identity mapping. Let [phi] : H x H [right arrow] R [union] {+ [infinity]} be a lower semicontinuous, [eta]-subdifferential, proper functional on H (may not be convex) satisfying [mathematical expression not reproducible] such that

Theorem 2.2 is easily implied by the recent result using the

identity mapping instead of [psi], [phi](t) = kt for t [greater than or equal to] 0 and considering the constant function [alpha]([OMEGA]) = 1 for W [member of] [M.sub.E].

When S is an

identity mapping on X, we obtain the corresponding definition for a (single) mapping satisfying the property (E.A) (see [14]).

[Id.sub.[S.sup.I.sub.G(L)]) is the

identity mapping of S(G) (resp.

where [mathematical expression not reproducible] is the resolvent operator of maximal monotone operator A, I is the

identity mapping and {[r.sub.n]} [subset] (0, to) is a regularization sequence.

Infoblox Inc., the network control company, today announced Infoblox

Identity Mapping, which bridges the gap between network security and user identity by intelligently correlating two previously separate sets of data, making it easier for network administrators to locate the source of security events, track mobile devices, monitor network usage and more.

Version 5.0 supports Sun's Solaris(TM) 10 Operating System (OS) and OpenSolaris(TM) OS, and includes a number of compliance features for regulatory requirements and standards such as PCI and Sarbanes Oxley, as well as industry-leading flexibility for

identity mapping, and support for Active Directory-based NIS (Network Information System) maps.