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Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces
Journal of Convex Analysis, 2006The aim of the paper is to extend to the setting of uniformly convex Banach spaces the results obtained for prox-regular sets in Hilbert spaces. Prox-regularity of a set C at a point x \in C
Bernard, Frédéric +2 more
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Journal of Optimization Theory and Applications, 2023
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On embedding trees into uniformly convex Banach spaces
Israel Journal of Mathematics, 1999The author deals with an investigation into the minimum value of \(D= D(n)\) such that any \(n\)-point tree metric space \((T,\rho)\) can be \(D\)-embedded into a given Banach space \((X,\|\cdot\|)\); i.e., there exists a mapping \(f: T\to X\) such that \(D^{-1}\rho(x,y)\leq\|f(x)- f(y)\|\leq \rho(x,y)\) for all \(x,y\in T\). Bourgain showed that \(X\)
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On a fixed point theorem on uniformly convex Banach spaces
1982Let \(K\) be a bounded closed convex subset of a Banach space \(X\), having normal structure (i.e. for every closed convex \(H\subset K\) there is an \(x\in H\) such that \(\sup \{\| y-x\|:y\in H\}
VEERAMANI, P, PAI, DV
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AMENABLE SEMIGROUPS OF NONLINEAR OPERATORS IN UNIFORMLY CONVEX BANACH SPACES
Bulletin of the Australian Mathematical Society, 2018In 1965, Browder proved the existence of a common fixed point for commuting families of nonexpansive mappings acting on nonempty bounded closed convex subsets of uniformly convex Banach spaces. The purpose of this paper is to extend this result to left amenable semigroups of nonexpansive mappings.
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Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 2013Let \(C\) be a bounded, closed and convex subset of a uniformly convex and uniformly smooth Banach space. Using some typical assumptions, the author shows that the generalized Mann and Ishikawa iterations converge weakly to a fixed point of an asymptotic pointwise nonexpansive map \(T\) from \(C\) to itself.
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State Dependent Sweeping Process in p-Uniformly Smooth and q-Uniformly Convex Banach Spaces
Set-Valued and Variational Analysis, 2012Messaoud Bounkhel, Charles Castaing
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Banach Spaces Which Can Be Given an Equivalent Uniformly Convex Norm
Israel Journal of Mathematics, 1972Per Enflo
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