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Interpolation of Uniformly Convex Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1982 If A 0 {A_0} and A 1 {A_1} are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [ A 0 ,
Michael Ćwikel, Shlomo Reisner
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Uniformly and locally convex asymmetric spaces
Russian Journal of Mathematical Physics, 2022 The author continues his investigation of uniform and local uniform convexity in asymmetric normed spaces initiated in [\textit{I. G. Tsar'kov}, Math. Notes 110, No. 5, 773--783 (2021; Zbl 1489.46022); translation from Mat. Zametki 110, No. 5, 773--785 (2021)].
Игорь Германович Царьков
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Iterative methods for monotone nonexpansive mappings in uniformly convex spaces
Advances in Nonlinear Analysis, 2021 We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed convex subset of an ordered uniformly convex space (X, ∣·∣, ⪯), T:C → C a monotone 1-Lipschitz mapping and x ⪯ T(x), then the ...
Shukla Rahul, Wiśnicki Andrzej
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Locally Uniformly Convex Banach Spaces [PDF]
Transactions of the American Mathematical Society, 1955 which we shall call local uniform convexity. Geometrically this differs from uniform convexity in that it is required that one end point of the variable chord remain fixed. In section I we prove a general theorem on the product of locally uniformly convex Banach spaces and with the aid of this theorem we establish that the two notions are actually ...
A. R. Lovaglia
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A uniformly convex hereditarily indecomposable banach space [PDF]
Israel Journal of Mathematics, 1997 A {\em hereditarily indecomposable (or H.I.)} Banach space is an infinite dimensional Banach space such that no subspace can be written as the topological sum of two infinite dimensional subspaces. As an easy consequence, no such space can contain an unconditional basic sequence.
V. Ferenczi
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Steepest Descent on a Uniformly Convex Space
Rocky Mountain Journal of Mathematics, 2003 This paper contains some generalizations of well-known results on the steepest descent method to find zeros or critical points of nonnegative \(C^2\) functions. The results known from the literature in Hilbert spaces are extended to uniformly convex Banach spaces. The theoretical findings are illustrated by two case studies.
M. Zahran
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Partial Mielnik spaces and characterization of uniformly convex spaces [PDF]
Proceedings of the American Mathematical Society, 1976 We characterize uniform convexity of normed linear spaces in terms of a functional inequality generalizing Clarkson’s inequality for L p {L_p} spaces. This inequality can be interpreted as saying that the unit sphere of the space carries a structure slightly weaker than a probability space in the ...
Andreas Blass, Č. V. Stanojević
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Some more uniformly convex spaces [PDF]
Bulletin of the American Mathematical Society, 1941 Let {Bi,i = l, 2, • . . } be a sequence of Banach spaces, and define B = P\Bi} to be the space of sequences b={bi} with biÇ^Bi and Ml = ( l > I N h ) 1 / p < °°> 1 < £ < °°. I t is known that B, normed in this way, is also a Banach space.
M. Day
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Journal of Function Spaces, 2015 The present paper is devoted to the study of the generalized projection πK:X∗→K, where X is a uniformly convex and uniformly smooth Banach space and K is a nonempty closed (not necessarily convex) set in X. Our main result is the density of the points x∗∈
Messaoud Bounkhel
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Applied General TopologyLet E be a uniformly convex Banach space and C a nonempty closed bounded convex subset of E. Let Γ : C ⟶ C and G : C ⟶ C be enriched strictly pseudocontractive mapping and Φ Γ -enriched Lipschitzian mapping respectively.
Imo Kalu Agwu +2 more
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