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On the New Hahn Sequence Space h(2)
Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.This paper investigates the properties and structural characteristics of the new Hahn sequence space defined by using the second‐order forward difference operator. First, we introduce the new Hahn sequence space: h2=x=xl∈ω:∑l=1∞l+1 Δ2xl<∞, liml→∞xl=0, of order two. Then, we show some topological properties of this new sequence space h(2), and calculate
Orhan Tuğ, Alberto Fiorenza
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Hahn-Banach Theorems for Convex Functions [PDF]
, 1998 We start from a basic version of the Hahn-Banach theorem, of which we provide a proof based on Tychonoff's theorem on the product of compact intervals. Then, in the first section, we establish conditions ensuring the existence of affine functions lying between a convex function and a concave one in the setting of vector spaces -- this directly leads to
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Fundamental theorems of functional analysis and applications
, 2016 Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: María Jesús Carro RossellAmong the fundamental theorems of Functional Analysis are the open mapping theorem, the closed graph theorem, the ...
Bastons García, Joan Carles
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On the Double Sequence Space Hϑ as an Extension of Hahn Space h
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space denoted as Hϑ, where ϑ ∈ {p, bp, r}, as an extension of the Hahn sequence space h.
Orhan Tuǧ +4 more
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Two-Rank and Atomic Solutions of a Bateman–Burgers Type Equation via Functional Analytic Methods
Journal of Applied MathematicsIn this paper, we derive both a two-rank solution and an atomic solution for a Bateman–Burgers type partial differential equation. Specifically, we study an equation in which the second mixed derivative of the unknown function with respect to space and ...
Waseem Ghazi Alshanti +2 more
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MathematicsWe start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorems and polynomial
Octav Olteanu
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A structural version of the theorem of Hahn-Banach [PDF]
We consider one of the basic results of functional analysis, the classical theorem of Hahn-Banach. This theorem gives the existence of a continuous linear functional on a given normed vectorspace extending a given continuous linear functional on a ...
Brinkhuis, J.
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Failure of the trilinear operator space Grothendieck theorem
Discrete Analysis, 2019 Failure of the trilinear operator space Grothendieck theorem, Discrete Analysis 2019:8, 16 pp. Let $\beta:\ell_\infty^n\times \ell_\infty^n\to\mathbb C$ be a bilinear form.
Jop Briët, Carlos Palazuelos
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GENERALIZATIONS OF THE HAHN-BANACH THEOREM REVISITED
Taiwanese Journal of Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dinh, N., Mo, T.
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Bishop-Phelps Theorem for Normed Cones
پژوهشهای ریاضی, 2019 Introduction In the last few years there is a growing interest in the theory of quasi-metric spaces and other related structures such as quasi-normed cones and asymmetric normed linear spaces, because such a theory provides an important tool in the study
Ildar Sadeghi, Ali Hassanzadeh
doaj