Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces

By Dan Butnariu, Alfredo Noel Iusem, Elena Resmerita. 2000

68 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9759c83a96a5c77b2db39073fbe7c5820529b381

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1. Dan Butnariu
2. Alfredo Noel Iusem
3. Frank Schöpfer
4. Tal Schuster
5. J. Vanderwerff
6. Alfred K. Louis
7. Alexander J. Zaslavski
8. Rolando Gárciga Otero

Citations in the corpus

• Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces (2003, background): “(31) and (35), we get jlðzT yn1Þj 8 1 , jlðyn2Þj 8 1 , and jlðzT SnxÞj 2 1 because klk ¼ 1: œ 502 Butnariu, Reich, and Zaslavski Now we are in a position to prove a result which shows that in the spaceMfu ðKÞ weak convergence of the orbits is a generic property.”
• Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces (2006, unknown): “This fact was proved in a particular case in [30] and the proof can be extended without much change.”
• Uniformly convex functions on Banach spaces (2008, background): “Ad-ditionally, related properties of convex functions and their applications have been studied in papers such as [2, 3, 4, 5].”
• Nonlinear iterative methods for linear ill-posed problems in Banach spaces (2006, background): “We now summarize and prove a few facts concerning p and its relationship to the norm in X (see also [1, 2, 4]).”
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces (2001, background): “[ 7 ]) X is smooth and uniformly convex, F is a singletonfzg, and f(x) =jjx zjjr with r > 1.”
• On Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces (2003, background): “For uniformly convex spaces sharper evaluations of νf (x, t) for f = ‖·‖ with r > 1 can be found in [16] and, in the particular case of X = L, even better estimates are given in [26].”
• An iterative regularization method for the solution of the split feasibility problem in Banach spaces (2008, background): “[1, 2, 6, 8, 10, 12–15, 18, 23, 26, 31, 32, 38, 43, 44, 46].”
• INEXACT VERSIONS OF PROXIMAL POINT AND AUGMENTED LAGRANGIAN ALGORITHMS IN BANACH SPACES (2001, background): “It has been proved in [14] that, for all r > 1, f r is Gâteaux differentiable when B is smooth (i.”
• ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES (2001, unknown): “) For total convexity, see [18].”