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Generalized Convexity and Generalized Derivatives
2006This chapter is devoted to the study of nonsmooth generalized convex functions with the help of special classes of generalized derivatives. Several results are presented on the links between generalized monotonicity of the generalized derivatives and generalized convexity of the functions under discussion.
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Automatic derivative generation
2013The inexact SQP method which we describe in Chapter 5 requires first and second order derivatives of the problem functions. There are several ways how derivatives can be provided. The first is to have them provided along with the problemdependent model functions by the user.
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On generalized (?,?)-derivations
2019We generalize the notion of (?,?)-derivation of Nakajima and Bres˜ar. We define the generalized (?,?)-derivations, generalized Jordan (?,?)-derivations, and generalized Lie (?,?)-derivations. We study interrelations between these classes of derivations as well as their homological properties.
Albas E., Argac N.
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Generalized Jordan Derivations
2001We define a notion of generalized Jordan (resp. Lie) derivations and give some elementary properties of generalized Jordan (resp. Lie) derivations. These categorical results correspond to the results of generalized derivations in [N]. Moreover, we extend Herstein’s result of Jordan derivations on a prime ring to generalized Jordan derivations.
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