Cover Image

Geometric Form of the Hahn–Banach Theorem for Generalized Convexity

We investigate a class of compact sets convex with respect to a certain family of planes. For compact sets that satisfy the condition of acyclicity of sections by a certain collection of two-dimensional planes, we prove their generalized convexity.

Saved in:

Bibliographic Details
Date:	2003
Main Authors:	Momot, I. V., Момот, И. В.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2003
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3906
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Klee Theorem for Linearly Convex Sets
by: Momot, I. V., et al.
Published: (2002)

On $(n, m)$-Convex Sets
by: Zelinskii, Yu. B., et al.
Published: (2001)

The Inverse Theorem for the Generalized Derivative in Banach Spaces
by: Радзієвська, Олена, et al.
Published: (2023)

Geometric entropy in Banach spaces
by: A. Dorogovtsev, et al.
Published: (2014)

A general form of generalized invertible operators on Banach spaces
by: V. P. Zhuravlov
Published: (2016)

A generalization of the Newton-Kantorovich theorem in a Banach space
by: S. M. Chuiko
Published: (2018)

On weak compactness of bounded sets in Banach and locally convex spaces
by: Kogut, P. I., et al.
Published: (2000)

On the Orthogonality of q-Classical Polynomials of the Hahn Class
by: Álvarez-Nodarse, R., et al.
Published: (2012)

Doubling (Dual) Hahn Polynomials: Classification and Applications
by: Oste, R., et al.
Published: (2016)

Turnpike theorems for convex problems
by: Mamedov, M. A., et al.
Published: (1996)

Central limiting theorem in the Banach space
by: Matsak , I. К., et al.
Published: (1988)

Hahn-Jordan decomposition as an equilibrium state of the conflict system
by: Koshmanenko, V. D., et al.
Published: (2016)

An Exactly Solvable Spin Chain Related to Hahn Polynomials
by: Stoilova, N.I., et al.
Published: (2011)

An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials
by: Ghressi, A., et al.
Published: (2011)

Hahn-Jordan decomposition as an equilibrium state of the conflict system
by: V. D. Koshmanenko, et al.
Published: (2016)

Simpson-type inequalities for geometrically relative convex functions
by: M. A. Noor, et al.
Published: (2018)

Simpson-type inequalities for geometrically relative convex functions
by: Awan, M. U., et al.
Published: (2018)

Tight Frame with Hahn and Krawtchouk Polynomials of Several Variables
by: Xu, Y.
Published: (2014)

On the Skitovich-Darmois theorem and Heyde theorem in a Banach space
by: Myronyuk, M. V., et al.
Published: (2008)

A note on the central limiting theorem in the Banach space
by: Matsak, I. K., et al.
Published: (1988)

On guestions of the general theory of convex functions
by: Perov, A. I., et al.
Published: (1966)

A Connection Formula of the Hahn-Exton q-Bessel Function
by: Morita, T.
Published: (2011)

Generalized convex sets and the problem of shadow
by: Vyhovs'ka, I. Yu., et al.
Published: (2015)

On the Lyapunov convexity theorem with appications to sign-embeddings
by: Kadets, V.М., et al.
Published: (1992)

On Certain Geometric Properties in Banach Spaces of Vector-Valued Functions
by: J.-D. Hardtke
Published: (2020)

On the Convex Pfaff-Darboux Theorem of Ekeland and Nirenberg
by: Bryant, Robert L.
Published: (2023)

Generalized convex sets and their applications
by: M. V. Stefanchuk
Published: (2017)

Estimation of the centroid Banach–Mazur distance between planar convex bodies
by: M. Lassak
Published: (2024)

Implicit Linear Nonhomogeneous Dierence Equation in Banach and Locally Convex Spaces
by: S. L. Gefter, et al.
Published: (2019)

Estimation of the centroid Banach–Mazur distance between planar convex bodies
by: Lassak, Marek, et al.
Published: (2024)

The Lyapunov theorem on convexity and its use for sign-embeddings
by: Kadets , V. М., et al.
Published: (1992)

Some theorems on stable convexity of closed curves under one-sheeted mappings
by: Cherneі, N. I., et al.
Published: (1971)

On the concept of generalized solution of operator equations in banach spaces
by: Petunin, Yu. I., et al.
Published: (1996)

Generalized convex sets and the problem of shadow
by: Ju. B. Zelinskij, et al.
Published: (2015)

Геометрическая форма теоремы Хана - Банаха для обобщенной выпуклости
by: Момот, И.В.
Published: (2003)

Теорема Кли для линейно выпуклых множеств
by: Момот, И.В.
Published: (2002)

Direct theorems of approximation for the functions regular in convex polygon by exponential polynomials in the integral metrics
by: Melnik, Yu. I., et al.
Published: (1988)

Inverse theorems of approximation of regular (in convex polygons) functions by exponential polynomials in the integral metric
by: Melnik , Yu. I., et al.
Published: (1988)

On the Generalized Cluster Algebras of Geometric Type
by: Bai, Liqian, et al.
Published: (2020)

Convergence of extrapolation from the past method for variational inequalities in uniformly convex Banach spaces
by: V. V. Semenov, et al.
Published: (2022)