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Uniformly convex and strictly convex Orlicz spaces [PDF]
AIP Conference Proceedings, 2016 In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.
Al Azhary Masta
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ON UNIFORMLY CONVEX AND UNIFORMLY 2-CONVEX 2-NORMED SPACES [PDF]
Demonstratio Mathematica, 1992 The author starts with the definition of two-norm on a linear space of dimension greater than 1 and defines a uniformly convex 2-normed space extending the definition of J. A. Clarkson. Theorems 1-5 and some corollaries are established on uniformly convex and uniformly 2-convex 2- normed spaces.
C.-S. Lin
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A uniformly convex hereditarily indecomposable Banach space [PDF]
Israel Journal of Mathematics, 1995 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.
Valentin Ferenczi
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Constructive reflexivity of a uniformly convex Banach space [PDF]
Proceedings of the American Mathematical Society, 1988 In this paper we consider a question about reflexivity of a Banach space within the framework of Bishop’s constructive mathematics and we give a partially affirmative answer to the question set by Bishop: "Is every uniformly convex Banach space reflexive?".
Hajime Ishihara
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Continuity of extremal elements in uniformly convex spaces [PDF]
Proceedings of the American Mathematical Society, 2009 In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex ...
Timothy Ferguson
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Strict Convexity and Uniform Convexity in Linear 2-normed Spaces
Journal of Harbin University of Science and Technology, 2021 Linear 2-normed space is a generalization of linear normed space, which defines a more extensive norm. In this paper, we get contraction mapping theorem in linear 2-normed space holds, and the set of fixed points for nonexpansive mapping is convex when ...
LI Shan-shan, CUI Yun-an
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Fixed point theorems in uniformly convex Banach spaces
Ratio Mathematica, 2023 In this article, we establish a concept of fixed point result in Uniformly convex Banach space. Our main finding uses the Ishikawa iteration technique in uniformly convex Banach space to demonstrate strong convergence.
Manoj Karuppasamy, R. Jahir Hussain
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UNIFORMLY CONVEX-TRANSITIVE FUNCTION SPACES [PDF]
The Quarterly Journal of Mathematics, 2009 We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces.
Rambla-Barreno, Fernando +2 more
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The generalized projection methods in countably normed spaces
Journal of Inequalities and Applications, 2021 Let E be a Banach space with dual space E ∗ $E^{*}$ , and let K be a nonempty, closed, and convex subset of E. We generalize the concept of generalized projection operator “ Π K : E → K $\Pi _{K}: E \rightarrow K$ ” from uniformly convex uniformly smooth
Sarah Tawfeek +2 more
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Convergence Theorems for an Iteration of Non-Lipschitzian Nonself Mappings in Banach Spaces
Nantong Daxue xuebao. Ziran kexue ban, 2021 In this study,a new iteration with errors for non-Lipschitzian nonself mappings in the uniformly convex Banach space is introduced.The convergence of such iteration is investigated and which proves that if the uniformly convex Banach space X satisfies ...
WU Li; YANG Hongli
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