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No-Dimensional Helly’s Theorem in Uniformly Convex Banach Spaces
Studia Scientiarum Mathematicarum HungaricaWe study the “no-dimensional” analogue of Helly’s theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach spaces: Helly’s theorem, fractional Helly’s theorem, colorful Helly’s theorem, and colorful fractional Helly’s theorem. The combinatorial part of the proofs for
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Fixed Point Theory and Applications, 2010 For a countable family of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-
Wangkeeree Rabian, Kamraksa Uthai
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Approximation of Solutions of an Equilibrium Problem in a Banach Space
Journal of Applied Mathematics, 2012 An equilibrium problem is investigated based on a hybrid projection iterative algorithm. Strong convergence theorems for solutions of the equilibrium problem are established in a strictly convex and uniformly smooth Banach space which also enjoys the ...
Hecai Yuan, Guohong Shi
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The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces
, 2016 Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either
Kim, Sun Kwang +2 more
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Every weakly compact set can be uniformly embedded into a reflexive Banach space
, 2009 NSFC [10771175]Based on an application of the Davis-Figiel-Johnson-PelzyA > ki procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space.
Zhang, W +14 more
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Fixed Point for Uniformly Local Asymptotic Nonexpansive Map
, 2023 Fixed points for uniformly local asymptotic nonexpansive maps are discussed in this article. An approximate fixed point sequence for such a map over a uniformly convex Banach space is derived.
Maiti, Pallab, Sultana, Asrifa
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Characterizations of almost transitive superreflexive Banach spaces [PDF]
, 2001 summary:Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth.
Palacios, Angel Rodriguez +1 more
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Continuity of metric projections in uniformly convex and uniformly smooth Banach spaces
Journal of Approximation Theory, 1983 The continuity of the metric projection onto an approximately compact set in a uniformly convex and uniformly smooth Banach space is investigated. The concept of directional radius of curvature at a point is defined: this allows the author to obtain an explicit modulus of continuity for the metric projection onto some sets (which are not necessarily ...
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Approximation of convex functions on the dual of Banach spaces
, 2002 This paper shows that every w*-lower semicontinuous Lipschitzian convex function on the dual of a locally uniformly convexifiable Banach space, in particular, the dual of a separable Banach space, can be uniformly approximated by a generically Frechet ...
Teng, Y. M. +3 more
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A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces [PDF]
, 2001 Let $varphi$ be a positive and non-decreasing function defined on the real half-line and ${mathcal U}$ be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banach space and satisfing a certain ...
Constantin Buse +3 more
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