By Robert R. Phelps
The enhanced and multiplied moment variation comprises expositions of a few significant effects that have been bought within the years because the 1st version. Theaffirmative solution by means of Preiss of the a long time outdated query of even if a Banachspace with an an identical Gateaux differentiable norm is a vulnerable Asplund area. The startlingly easy evidence by means of Simons of Rockafellar's basic maximal monotonicity theorem for subdifferentials of convex features. The fascinating new edition of the valuable Borwein-Preiss tender variational precept as a result of Godefroy, Deville and Zizler. the fabric is offered to scholars who've had a direction in useful research; certainly, the 1st version has been utilized in quite a few graduate seminars. beginning with convex features at the line, it results in interconnected issues in convexity, differentiability and subdifferentiability of convex capabilities in Banach areas, favourite continuity of monotone operators, geometry of Banach areas and the Radon-Nikodym estate, convex research, variational ideas and perturbed optimization. whereas a lot of this is often classical, streamlined proofs discovered extra lately are given typically. there are lots of workouts, a lot of which shape an essential component of the exposition.