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Convex Functions, Monotone Operators and Differentiability

Robert R. Phelps (Autor)

Buch | Softcover

XII, 120 Seiten

1993 | 2nd ed. 1993
Springer Berlin (Verlag)
978-3-540-56715-8 (ISBN)

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In the three and a half years since the first edition to these notes was written there has been progress on a number of relevant topics. D. Preiss answered in the affirmative the decades old question of whether a Banach space with an equivalent Gateaux differentiable norm is a weak Asplund space, while R. Haydon constructed some very ingenious examples which show, among other things, that the converse to Preiss' theorem is false. S. Simons produced a startlingly simple proof of Rockafellar's maximal monotonicity theorem for subdifferentials of convex functions. G. Godefroy, R. Deville and V. Zizler proved an exciting new version ofthe Borwein-Preiss smooth variational prin ciple. Other new contributions to the area have come from J. Borwein, S. Fitzpatrick, P. Kenderov, 1. Namioka, N. Ribarska, A. and M. E. Verona and the author. Some ofthe new material and substantial portions ofthe first edition were used in a one-quarter graduate course at the University of Washington in 1991 (leading to a number of corrections and improvements) and some of the new theorems were presented in the Rainwater Seminar. An obvious improvement is due to the fact that I learned to use '!EX. The task of converting the original MacWrite text to '!EXwas performed by Ms. Mary Sheetz, to whom I am extremely grateful.

Convex functions on real Banach spaces.- Monotone operators, subdifferentials and Asplund spaces.- Lower semicontinuous convex functions.- Smooth variational principles, Asplund spaces, weak Asplund spaces.- Asplund spaces, the RNP and perturbed optimization.- Gâteaux differentiability spaces.- A generalization of monotone operators: Usco maps.

Erscheint lt. Verlag	29.7.1993
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 120 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 242 mm
Gewicht	214 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Analysis • Calculus • Convex Functions • Convexity • Differentiability • differential equation • Hardcover, Softcover / Mathematik/Analysis • Maximum • Monotone Operators • Optimization
ISBN-10	3-540-56715-1 / 3540567151
ISBN-13	978-3-540-56715-8 / 9783540567158
Zustand	Neuware